Maxwell hammered 95 off 43 balls while Miller made an unbeaten 54 off 37 to propel their team past Super Kings' imposing 205 for four with seven balls to spare at the Sheikh Zayed stadium.
Virender Sehwag (19 off 10) and Cheteshwar Pujara (13 off 10) started Punjab's chase aggressively before departing in quick sucession.
Offie Ravichandran Ashwin, who trapped Pujara in front of the stumps, earned his second lbw by foxing Akshar Patel (2), leaving Punjab at 53 for two in sixth over.
The deadly duo did not disapppoint as they took the Super Kings bowlers to the cleaners. Maxwell scored the bulk of the runs in their 63-ball stand and was also at his cheeky best.
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The Australian all-arounder enthralled the crowd with his switch hits and hoicks over mid-wicket. Like Miller, who was dropped off Ravindra Jadeja in the ninth over, Maxwell also had the luck on his side. The result could have been different had the Australian not been dropped twice.
Miller got into the groove after Maxwell's fall and got his side closer to the target by smashing Jadeja for two consecutive sixes. With captain George Bailey (17 off 10) at the other end, Punjab eventually strolled to a morale boosting victory.