Andre Russell who scored an unbeaten 49, bagged 3/22 later.
Cummins has returned to his home in Australia for two weeks of rest and rehabilitation.
The entry of Knight Riders group makes them the sixth team to own a team in the tournament and their fourth overall investment in a T20 League after the IPL, Carribean Premier League and Major League Cricket.
Barring a 43-ball 51 from Ishan Kishan, Mumbai batters struggled to get going in the chase as their innings ended at 113 all out in 17.3 overs.
KKR were bowled out for 101 runs chasing Super Giants total of 176/7.
Sanju said with his batters failing to master the KKR bowling on a slow track, they fell short by 15-20 runs.
Nitish Rana and Rinku Singh remained unbeaten on 48 and 42 runs for KKR.
Released by KKR ahead of the ongoing season, Kuldeep has thrived at Delhi claiming 17 wickets in eight matches equalling his 2018 haul from 16 games.
The Capitals chased down a target of 147 in the 19th over.
Russell, who bagged 4/5 also scored 44 off 25, but the Titans secured an 8-run win.