Led by a Vintage Virat Kohli innings and garnished by a strong Maxwell finish, RCB defeated GT by 8 wickets to stay alive on Thursday.
This was after skipper Hardik Pandya scored a gritty 47-ball 62 to lift GT to a competitive 168 for five after opting to bat.
Kohli (73 off 54) and captain Fa du Plessis (44 off 38) shared a match-winning 115-run opening stand before Glenn Maxwell (40 not out off 18) went ballistic to ensure the team got home in 18.4 overs.
By virtue of this win, RCB moved to fourth place in the standings with 16 points but will have to wait for the Delhi Capitals-Mumbai Indians game on Saturday to know their fate. A loss for Delhi would ensure RCB a play-off berth.
As the 'Kohli Kohli' chants suggested, the whole of Wankhede and probably the country wanted to see the former India captain back amongst the runs and with a little bit of luck going his way, he was back playing the shots he is known for.
When Kohli picked Mohammed Shami for two lofted boundaries over the bowler's head and cover in the third over, it looked like it would be his night. His next four was a streaky one off Hardik who bowled with the new ball.
The very next ball, Kohli was at his animated best as he whipped Hardik towards square leg with Rashid Khan missing a tough chance in the deep.
A sign of his growing confidence was an aerial straight drive off Rashid. Kohli was quick on his feet both against Rashid as well as the pacers. The Indian superstar brought up his second fifty of the season by whipping a full ball off Rashid over deep midwicket.
With Kohli on song, Du Plessis played his part perfectly and kept rotating the strike besides an odd boundary.
After the captain's dismissal, Maxwell joined Kohli and went ballistic from ball one. The Australian's cameo included a reverse scoop shot off Hardik that went all the way.
After collecting his second six off Rashid, Kohli tried one too many and got stumped in the 17th over but the job had been well and truly done by then.
Earlier, Hardik lifted GT to a competitive total. Coming into the game with a string of low scores, he warmed up nicely for the playoffs with a well crafted fifty even though he was not at his fluent best.
RCB limited GT to 72 for three in 10 overs, largely due to their brilliance in the field despite Wriddhiman Saha's (31 off 22) threatening stay in the middle.
Saha provided another brisk start with some clean hitting but his opening partner Shubman Gill perished cheaply. The right-hander poked at a good length ball and Maxwell, standing at a widish first slip, plucked a stunning one-handed catch diving to his right.
Matthew Wade, who has not been at his explosive best in the IPL, fell to a controversial call which also attracted empathy from Kohli. Wade was sure that he underedged a sweep shot off Maxwell and took no time in reviewing the on-field decision, which was out.
However, despite a clear deviation in the ball's trajectory before it thudded onto the pads, the UltraEdge did not detect it and the TV umpire stayed with the on-field umpire's call. Wade had no choice but to grudgingly walk back into the dugout.
Saha, who hit four boundaries and a six, had Hardik for company in the middle but following a mix up with his captain, the wicketkeeper fell way short of his crease when Du Plessis came up with a stunning direct hit from mid-off.
Hardik, who was dropped on 14, made it count alongside David Miller (34 off 25), who continued his impressive run in the tournament.
Miller smashed three sixes before Wanindu Hasaranga got rid of him with a sharp return catch.
Rashid (19 not out off six) joined Hardik in the death overs and did what he has done throughout the season. The leg-spinner whacked a couple of sixes towards the end to push the total past 160.