Stormers, from South Africa, ended the league phase of the competition at the head of the table on 66 points, two clear of New Zealand's Waikato Chiefs.
The Stormers, who will host a semi-final and the final if they get there, had to repel a strong second-half performance from the Australian visitors who trailed 16-0 at half-time before clawing their way back with three tries.
However, it was not enough to provide former Australia international Stirling Mortlock, an 80-Test veteran, with a winning swansong in the 35-year-old's last game before retiring.
The Stormers played the first half with a strong wind at their backs and made all the early running as two penalties from fly-half Peter Grant put them 6-0 ahead after eight minutes.
Grant ended the match with 16 points courtesy of two conversions and four penalties in a flawless kicking display.
The home team continued to build on their territorial advantage and they grabbed their first try, in the 14th minute, when outside centre Juan de Jongh stepped off his left foot to beat two defenders.
The Rebels fought back and they had the better of the second quarter of the match but were unable to breach a Stormers defence which had, before the game, conceded just 18 tries all season.
The hosts had the final say in the half as Grant succeeded with his third penalty on the stroke of halftime.
The Rebels made an impressive start to the second half and they finally broke through the Stormers' defence, in the 50th minute, when loose-head prop Rodney Blake dived over from close-range for a converted try.
The visitors had only won four games coming into the match but they belied their lowly log position by scoring their second try four minutes later when scrum-half Nick Phipps scooped up a loose ball before crossing from three metres out.
Full-back Julian Huxley nailed the conversion to leave the Rebels trailing by just two points.
But the Stormers were stung into action and De Jongh grabbed his second try almost immediately after the restart when he ghosted through a gap in the Rebels' defence.
The Rebels were not prepared to give up and, with 10 minutes left, replacement scrum-half Nic Stirzaker set up a try for fellow substitute Cooper Vuna after the halfback threw an outrageous dummy before a searing midfield break split the Stormers' defence wide open.
But the Stormers finally sealed the victory when Grant nailed a penalty with four minutes left.
The Sharks defeated the Cheetahs 34-15 at Kings Park to qualify for the play-offs at the expense of the Wellington Hurricanes.
The bonus point win moved the Sharks from eighth to fifth place, knocking the Hurricanes out of the knockout stages.
They were forced to work hard for their win after trailing 6-15 at half-time but they then ran in four tries in a superb second-half performance while the visitors failed to add to the five first-half penalties from fly-half Riaan Smit.
Sharks pivot Frederic Michalak ended with 14 points courtesy of four conversions and two penalties.
"It was a nerve-wracking first 40 minutes but we hung in there and didn't let them score any tries and we were still in it at halftime," Sharks captain Keegan Daniel said in a televised interview.
Neither team were able to establish an early advantage in a scrappy first half with Michalak and Smit trading early penalties.
But the Sharks made life difficult for themselves when inside centre Francois Steyn was yellow-carded for a spear tackle on Cheetahs centre Robert Ebersohn in the 19th minute.
Smit kicked the visitors into the lead from the resulting penalty before succeeding with his third penalty, in the 24th minute.
Michalak narrowed the gap with his second penalty but the Cheetahs were punishing the Sharks for their lack of discipline and Smit kicked his team into what seemed like a commanding half-time lead with two more penalties.
The Sharks opted to run a penalty four minutes after the restart and their endeavour was rewarded when flank Daniel dummied his way over from close-range for a converted try to reduce the deficit to two points.
The hosts took the lead for the first time in the match in the 59th minute when right wing JP Pietersen set off on a searing 35-metre run before putting in a deft chip kick which was collected by scrum-half Charl McLeod who went over for a converted try.
The Sharks were running rampant and two minutes later flank Marcell Coetzee grabbed a well-deserved try when he burst clear from 30 metres out.
The home team wrapped up the bonus point for scoring four tries six minutes before the end of the match when a turnover ball on the halfway line went through four pairs of hands before number eight Ryan Kankowski sprinted clear to score.
The Bulls raised their game in the second half to beat struggling neighbours the Lions 37-20 and qualify for a playoff against the Crusaders in Christchurch.
The three-times champions struggled in the first half, which ended with the scores level 20-20, but rallied to score two tries in the first 10 minutes of the second to set up victory and clinch fifth place in the final standings.
The Lions, with relegation from Super Rugby hanging over their heads, came out roaring for their possible last appearance, dominating the Bulls in the scrums and breaking through tackles.
But they were once again frustrated by the errors that have characterised their campaign, Bulls wing Akona Ndungane taking advantage of flatfooted passing down the back-line to intercept and score the opening try in the 16th minute.
Lions fly-half Elton Jantjies kicked two penalties to keep the visitors in touch at 6-10 down until the half-hour, when their defence failed, two men going for Bulls scrum-half Francois Hougaard as he darted from the base of a five-metre scrum, allowing wing Bjorn Basson to burst through a huge gap and score.
The Lions were trailing 6-17, but they bounced back superbly as tenacious scrum-half Michael Bondesio ran straight through Bulls flyhalf Morne Steyn to score from a five-metre scrum and, although the visitors then presented Steyn with an easy penalty after a ruck infringement, an excellent dash down the left touchline by wing Anthony Volmink gave the Lions a line-out feed five metres from the tryline.
The Lions had struggled to secure their own lineout ball throughout the first half, but this time lock Hendrik Roodt took the ball and captain Josh Strauss was at the front of the drive over the line.
Jantjies converted the try from the touchline to draw the Lions level and leave the Bulls needing a much-improved second half to keep their campaign alive.
The Lions had an early reprieve in the second half when a Steyn penalty hit the upright, but the Bulls forwards stepped up their intensity and simply overwhelmed the Lions, who were unable to get out of their own territory.
Four minutes after the break, outside centre JJ Engelbrecht went on a superb, mazy run, while hooker Chiliboy Ralepelle punched the ball up well in midfield to set up a ruck, from which Hougaard broke and ran in a try from 25 metres out.
Four minutes later, the Lions were powerless to stop a succession of forward drives by the Bulls, with flank Jacques Potgieter having an easy run-in for the try.
Full-back Zane Kirchner, under pressure from front-rankers Martin Bezuidenhout and JC Janse van Rensburg, made a mess of dotting down for a fifth try in the 60th minute, but the Springbok then won an up-and-under to set up another penalty for Steyn that completed the scoring.