Batting first, De Villiers' master class and Maxwell's counter-attacking half-century propelled RCB to an imposing 204 for four. In reply, KKR were stopped at 166 for eight as RCB regained the top spot in the pecking order.
RCB smashed 56 runs in the last three overs, including 21 in the final six deliveries, thanks to de Villiers 34-ball 76 not out.
Maxwell blazed away to 78 off 49 deliveries, hitting nine boundaries and three maximums before the genius from South Africa strode in and struck the same number of fours and sixes as his teammate from Australia.
The Knight Riders were off to a brilliant start with leg-break bowler Varun Chakravarthy leaving RCB in early trouble at 9/2 with the big wickets of skipper Virat Kohli (5) and Rajat Patidar (1) in the second over.
Opening the bowling for KKR, veteran off-spinner Harbhajan Singh bowled a tight line and length to stifle the RCB batsmen in his first two overs.
After Chakravarthy lured Kohli to go over cover with a tossed-up delivery that drifted away from the right-hander, Rahul Tripathi pulled off a sensational catch running back from extra-cover. The top batsman was nowhere close to the ball.
Chakravarthy then went through the defence of Patidar with one that darted back on landing.
Mixing aggression with caution, Maxwell and Devdutt Padikkal (25) revived the RCB innings after the early blows at the MA Chidambaram Stadium.
While the young Indian seemed content playing the second fiddle, the swashbuckling Australian counter-attacked in fine fashion and played the big shots with consummate ease.
The in-form Maxwell upped the ante when he cleared his front leg to plonk Shakib Al Hasan over long-on for his first maximum in the sixth over.
The one bowled by Shakib turned out to be a productive over for RCB as they got 17 runs off it.
Morgan's decision to take out both Chakravarthy and Harbhajan at a time when they were bowling well was baffling, but RCB didn't mind at all as they capitalised on the surprising move.
After reaching 45 for two at the end of the six powerplay overs, Maxwell shifted gears and raced to his half-century in just 28 balls. Even Chakravarthy, who was on fire some time ago, was not spared by Maxwell as he smashed him for a six and four off successive balls.
Prasidh Krishna ended the third-wicket partnership of 86 runs by sending back Padikkal, which signalled the arrival of De Villiers in the middle.
Joining forces, the dazzling duo of Maxwell and De Villiers did not allow the KKR bowlers to settle into any sort of rhythm until premier pacer Pat Cummins ended their 53-run association.
After that, the show belonged to De Villiers as he toyed with KKR bowlers.
He finished it off in style, pummelling Andre Russell for three fours and a six in the last over of the innings.
The last-over onslaught was preceded by 4, 4, 6 as de Villiers left poor Russell bruised and battered.
The extremely-talented Shubman Gill and in-from Nitish Rana struck a few fours and sixes before the former got out for a nine-ball 21.
KKR kept losing wickets at regular intervals and were tottering at 114 for five in the 14th over when purple cap holder Harshal Patel dismissed captain Eoin Morgan (29).
Russell (31 off 20 balls) provided some entertainment by collecting 20 runs off Yuzvendra Chahal in the 17th over, the sequence of shots reading 6, 4, 4, 4.
Next, Kyle Jamieson was played over midwicket for a big six by Russell, but the tall Kiwi pacer also had two wickets in the same over.
For RCB, Jamieson finished with 3/41 and there were two wickets apiece for Harshal and Chahal.