Imran Khan, Lloyd Norris Jones and Rupinder Pal Singh scored for the home team while Mumbai skipper and drag-flick specialist Sandeep Singh struck thrice to push his tally to nine goals, the highest so far in the tournament.
The win keeps Delhi on top of the standings with 27 points from six games as Mumbai lie at the bottom on six points.
The playing style of both teams was on expected lines. Delhi, led by star player Sardar Singh, passed the ball to create chances while the visitors relied heavily on penalty corner conversion.
Delhi were aggressive from the word go, penetrating into the strike zone without much resistance from Mumbai's brittle defence.
Imran got Delhi ahead in the fifth minute, deflecting a neat pass from Gurwinder Chandi. Man of the match Norris Jones made it 2-0 in the 12th minute through a rebound coming from a goalkeeper's save.
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The South African netted another one early in the second quarter with help from Danish Mujtaba, who pulled off a brilliant run to enter the D and pass it to Lloyd Jones. Sandeep Singh converted Mumbai's first penalty corner in the 28th minute.
The third quarter did not see much action barring Rupinder's grounded strike from a penalty corner, making it 4-1 for Delhi.
Mumbai made a heartening comeback in the last quarter with their captain scoring twice. The equaliser seemed very much on the card but Delhi eventually held on to their slender advantage.
A sizeable crowd witnessed the action on India's Republic Day and their presence was appreciated most by Sardar.