The match ended at 2-1, giving the hosts their second win in as many games.
Rupiner Pal Singh and South Africa's Lloyd Norris Jones made it 2-0 for Delhi while drag-flicker Sandeep Singh pulled one back for Mumbai at the Major Dhyan Chand Stadium.
But Sandeep soon became a villain when he failed to score off a stroke in the 70th minute.
The hard-fought win was Delhi's second straight one at home after they beat Punjab Warriors Monday.
They now have 10 points in their kitty.
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Sardar Singh was named man of the match.
Mumbai, playing their opening match of the competition, relied more on counter attacks.
Delhi, on the other hand, were better in planning and constantly penetrated into the strike zone.
They had the bulk of the possession in the first quarter but could only find the net in the 27th minute with Rupinder Pal scoring off their second penalty corner.
The next quarter witnessed exciting play from both teams. Norris Jones, who missed easy scoring opportunities earlier, did well this time to guide the pass beyond the opposition goalkeeper in the 48th minute.
Mumbai hit back in the 50th minute on counter attack, giving them a penalty corner which Sandeep Singh converted with ease.
The matched reached its climax in the final quarter until Sandeep made a mess of the penalty stroke.
He claimed a goal after his flick landed near the goal line but the umpire quickly ruled that out.
The spectator count dropped significantly from the tournament opener here Monday but the atmosphere remained lively, thanks to a handful of fans who danced all the way.