The league's top scorer Mandzukic, unfazed by media reports Bayern are close to signing Borussia Dortmund forward Robert Lewandowski for next season, snatched his 15th goal of the campaign in dazzling fashion in the 36th minute.
Substitute Robben then drilled the ball in from six metres in stoppage time at the end of the game as Bayern continued their spectacular assault on a first league title since 2010.
They have won 18 of their 22 matches this season including their last five away from home. The Bavarians have also not conceded a goal since the league resumed in January following a mid-season break.
Bayern, who visit Arsenal in the Champions League last 16 next week, have 57 points. Champions Borussia Dortmund, second on 39, host Eintracht Frankfurt on Saturday when third-placed Bayer Leverkusen also entertain lowly Augsburg.
"Wolfsburg certainly battled very hard," Bayern coach Jupp Heynckes said.
"It was tough and it is these games we must win. We did just that and showed we are a top team."
The teams set a fierce tempo early on with Thomas Mueller heading over the bar for the visitors and Wolfsburg's Bas Dost failing to connect with a good chance in the box.
Bayern showed off their quick-passing style and took the lead when Croatia striker Mandzukic, again preferred to Mario Gomez, headed in after Bastian Schweinsteiger set him up.
Mandzukic, who did not celebrate his goal against the club he represented from 2010-12, also had a shot cleared off the line by Naldo in the 49th minute.
Wolfsburg worked hard for an equaliser and came agonisingly close with a curling Diego free kick in the 77th minute that was expertly palmed away by Manuel Neuer as it headed for the top corner of the net.
Unmarked Dutch winger Robben, hindered by injury this season, completed the victory late on as Wolfsburg remained in 12th place on 26 points.
"We gave it all we had and it was an evenly-balanced game in the second half," said Wolfsburg coach Dieter Hecking.
"Bayern are more efficient. We need to continue working as we have but we have become more stable as a team," added Hecking who took charge in December.