The Delhi side took the lead in the 29th minute through young striker Talwinder Singh's field goal from the top of the opposition circle to stun the large number of home crowd present at the newly-built International Hockey Stadium.
But Waveriders' joy was shortlived as Affan Yousuf equalized for Warriors four minutes later by scoring from a goal-mouth melee.
Wilson restored Delhi's lead in the 47th minute with a strike from close range after he was set up by Akashdeep Singh.
Thereafter, the home pressed hard for the equalizer but the Waveriders defended stoutly to thwart any danger to their goal.
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The Waveriders sealed the contest in their favour when Wilson scored his second goal of the day just two minutes from the final hooter.
The Waveriders will next travel to Ranchi where they will face holders Ranchi Rhinos on Monday, while Punjab Warriors will host Mumbai Magicians at the same venue tomorrow.
With this win the Sardar Singh-led Waveriders, last year's most consistent team, have pocketed five points from the encounter, while the Warriors secured one point despite the loss because, as per the tournament rules, a defeat with goal difference of two or less goals will give the losing side one point.