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.
Minutes later, Punjab Warriors got a penalty corner but their star drag-flicker was off the target.
Thereafter, the home pressed hard for the equalizer but the Waveriders defended stoutly to thwart any danger to their goal.
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 on Sunday.
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.
Narinder Batra, Chairman, Hero HIL, said, " When we started Hockey India League, we were not sure how will the League be accepted by the audience and fans. But after the tremendous success of 2013, this year we saw many Corporate coming forward and showing enthusiasm in associating with the game and believing in our faith."
The laser show depicted a short montage on HIL and the six franchisees. It showed the first edition of HIL with its results, goals scored by various players amongst other action from the inaugural tournament.
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