Brecel, who beat Ricky Walden and Mark King in the previous rounds, twice looked to have the match in his pocket but missed a simple pink with only the final two balls remaining at 5-4 up before repeating the feat in the decider after running out of position on the blue.
The 2008 champion now goes on to the semis where he will meet Ali Carter, who earlier beat Stuart Bingham 6-4 in another close encounter.
Brecel, ranked 74th in the world, started confidently with visits of 39 and 41 enough to secure the opening frame. A scrappier second followed with the black covering the corner pocket and the safety exchange inevitably pushing the reds to the same side of the table. Brecel looked to have made a fatal error after falling short in trying to lay a snooker behind the green but having escaped his own snooker, a brilliant shot to nothing to pot the red into the centre pocket off two cushions looked to have the frame won before a simple missed red let Murphy off the hook.
His tail up, a second century break of the tournament, a 122, put Murphy in front for the first time. But a well constructed 47 break in the next pulled Brecel level at the interval after Murphy failed to escape four snookers.
Murphy looked to be well on course to take a 3-2 lead when an unfortunate contact put him out of position. But another miss from Brecel allowed Murphy to re-establish his lead before Brecel hit back with a heavy scoring visit to level matters at 3-3. A break of 48 proved enough for Brecel to sneak back ahead but a composed 79 saw Murphy again draw level.
A quite superb 64 break with the black out of commission in its entirety saw Brecel get to within a frame of victory. An understandably tense 10th followed and it was the youngster who held his nerve better in winning a lengthy safety exchange against his more experienced opponent. But with the frame and match seemingly at his mercy, a nudge on the green put him out of position on his penultimate red.
Still Brecel had one glaring chance to book his semi-final spot after Murphy left the blue over the middle pocket. Having negotiated the blue, the remaining two balls would have been a formality under normal circumstances but Brecel blinked for the first time, wriggling the pink in the jaws and leaving it for Murphy to take the match to a decider.
Brecel had the first chance but with the adrenaline coursing through his veins and his break on 26, he overscrewed a red with the rest. The mistake looked to have cost him but Murphy was down on his shot too quickly and left the red over the corner pocket. With the brown on its spot and the remaining four colours in perfect position, inexperience again got the better of Brecel. He finished the wrong side of the blue and left himself a tough long pink under any circumstances. It rattled in the jaws, leaving Murphy to polish off and breathe a huge sigh of relief.
Despite his heartbreaking defeat, Brecel has won a host of new fans and breathed fresh life into a tournament missing Ronnie O’Sullivan and reeling from the first round exit of Judd Trump. The world of snooker may well have found a new star.
The earlier finishing match also produced a nail biting match. Carter was in first with a 38 but a loose safety allowed Bingham to respond with a fluid 74 to clinch the opener.
Carter responded in fine style with a quite brilliant 134 clearance to draw level and a 46 break was enough to edge him into the lead for the first time. Bingham was in first with a 25 in the next but a miss whilst amongst the balls let Carter in for a 68. Successive Carter errors let Bingham in the balls again and he looked favourite to level at the break before going out of position on the brown with just the colours remaining. Carter knocked off the brown and blue to take a two frame advantage.
Bingham hit back to win the first on resumption but Carter established his two frame advantage with breaks of 28 and 23 proving good enough. The newly-crowned Premier League champion avoided going three down with four to play with a gutsy 79 break to stay one behind at 4-3 and two scoring visits were enough to draw Bingham level and set up a big finish.
Carter won a scrappy eighth thanks to a 60 break and a superb final red along the rail booked his place in the last four despite Bingham playing on for three snookers off the final pink.