Chasing an imposing 192 to win, Maxwell and Miller put on display an incredible power-hitting show as Punjab overhauled the target with eight balls to spare.
Young batsman Sanju Samson (52) hit a classy half-century and Shane Watson (50) played a captain's knock to guide Rajasthan Royals to 191 for five after being put into bat but their effort proved little.
It was Maxwell, who yet again played a gem of a knock, turning the match on its head with sensational hitting.
Maxwell's knock came off just 45 balls as he punished the bowlers with eight fours and six sixes. He did not spare a single Rajasthan bowler as it rained boundaries when he was batting in full flow.
The rivals bowlers were left clueless where to bowl as the Australian dealt only in fours and sixes. In 10 overs, Punjab were 69 for two but in the next three overs, Punjab scored 51 runs with Maxwell scoring 46 of them.
Maxwell hit nine boundaries, including two sixes, in those three overs, which changed the complexion of the game.
In his third-wicket partnership of 116 runs with Cheteshwar Pujara, Maxwell's contribution was 89 while Pujara (40 not out) was reduced to a spectator at the other end.
Kane Richardson stemmed the rot by dismissing Maxwell and that time Punjab needed 66 off 37 balls. Left-handed Miller carried forward the good work with magnificent batting.
Miller hit four sixes off the paceman Dhawal Kulkarni as Punjab creamed off 27 runs in the 18th over. It was all over for Rajasthan in that over.
Punjab were actually off to a poor start as Virender Sehwag (2) yet again departed early. Sehwag hit his shot well off Kulkarni but found the fielder. Wriddhiman Saha (2) was scalped by James Faulkner and Punjab were reduced to 10 for two.
Maxwell took the fight to the rival camp with his fearless batting. He quickly completed his fifty while opener Pujara was holding the one end carefully.
Playing reverse sweep with amazing success in his innings, Maxwell hit Rajat Bhatia for two consecutive boundaries to raise his fifty in 28 balls.