Chasing 163 for victory on a tricky pitch, Sudharsan (62) and fellow left-hander Miller (31) put together an unbeaten stand of 56 to steer their team home with 11 balls to spare in Delhi.
Gujarat were in early trouble after an excellent spell of fast bowling by South African Anrich Nortje, but Sudharsan stood firm in his team's second straight victory this season.
One of the South African players to have joined the IPL for this match after the Netherlands one-day international series, Miller, who replaced the injured Kane Williamson in the XI, played his part with a 16-ball blitz.
Gujarat pace spearhead Mohammed Shami and leg-spinner Rashid Khan took three wickets each as they restricted the opposition to 162-8 before handing Delhi a second straight loss.
Gujarat did not have the best of starts as Nortje removed both openers, including bowling Shubman Gill for 14, and were in further trouble when left-arm quick Khaleel Ahmed got skipper Hardik Pandya caught behind for five.
But Vijay Shankar replaced Ireland fast bowler Josh Little under the new "impact player" rule introduced this season and joined Sudharsan in the middle to revive the chase.
Mitchell Marsh broke the dangerous-looking stand of 53 after he trapped Shankar lbw for 29 but Sudharsan and Miller completed the job.
Below-par batting
Delhi's batsmen never really got going despite skipper David Warner's 37 and a quickfire 36 from Axar Patel as they posted a below-par total.
Shami struggled to control his line and length and gave away runs at the start before he found his groove with the two key wickets of Prithvi Shaw and Marsh.
Warner fell to Alzarri Joseph as he chopped on to his stumps.
Joseph bowled at a lively pace and dismissed Rilee Rossouw for a first-ball duck.
Rashid claimed the wicket of Sarfaraz Khan who struggled to a 34-ball 30.
Coming in at number seven, Axar took on the bowlers with three sixes and two fours in his 22-ball innings but could not haul Delhi to a big enough total.
