Chasing a modest 147 for a win, KKR lost a few early wickets but Gambhir (60) and Yusuf Pathan (40 not out) stitched a 65-run fourth wicket stand to help the defending champions canter home in 18.1 overs.
DD, who had bounced back with two wins -- Kings XI Punjab and SunRisers Hyderabad -- after snapping their 11-match losing streak, suffered their ninth home loss in over three editions starting 2013.
New-ball bowler Dominic Muthuswami struck twice in his second over to first get Robin Uthappa caught at mid-off and three balls later Manish Pandey (0) helped a short-ball into the hands of Imran Tahir at third man.
Nathan Coulter-Nile also bowled well to get Suryakumar Yadav (24) caught behind and break a 48-run third wicket partnership.
But then Gambhir, who hit eight boundaries in his 49-ball stay, and Yusuf, who struck six fours and a six in his 26-ball knock, made things look simple as Delhi continued to juggle their bowlers without much effect.
Champion leg-spinner Tahir did clean up Gambhir in the 18th over but it was too late in the day as Pathan stayed on to see Ryan ten Doeschate (2) get the winning runs.
Earlier, KKR bowlers led by Morne Morkel and Umesh Yadav bowled a tight line to restrict the Jean-Paul Duminy-led side to 146 for eight in 20 overs.
Put into bat, DD were hurt by lack of partnerships but a late flourish from Angelo Mathews (21-ball 28) helped the home side get some respect as Morkel, Yadav and Piyush Chawla picked two wickets apiece.