Former Leeds Rhinos star Burrow, 41, died last week after a battle with motor neurone disease, leading to an outpouring of emotion across Britain.
Burrow's shirt number seven was projected onto giant screens inside and outside Wembley and as a further tribute, the men's final kicked off at 3:07 pm.
When the action started, reigning Super League Man of Steel Bevan French set up Zach Eckersley for Wigan's opening try and stretched over for the second himself to ensure his side also became the first team since 2007 to hold all four of the game's major honours at once.
Warrington rallied and Matt Dufty's late try gave them a glimmer of hope but they were second-best throughout and seldom looked likely to win the trophy for head coach Sam Burgess in his first season in charge.
Burrow's name and image adorned a large banner near Wembley and fans laid scarves and flowers at a rugby league statue outside the stadium in tribute to the former Leeds number seven, who won two Challenge Cup finals.
The crowd of nearly 65,000 rose for a minute's silence before kick-off and again seven minutes into the match in honour of the shirt Burrow wore.
Wigan scored their opening try in the 19th minute when French delivered the ball into the path of Eckersley, who shrugged off Matty Ashton to touch down.
Ashton's knock-on three minutes later from Harry Smith's high ball kept Warrington pinned back and led to Wigan's second try, Abbas Miski and Jai Field stretching the opposition defence before French touched down following a scrum.
Liam Farrell marked his fifth final by scoring Wigan's third try and Smith's third conversion gave Matt Peet's men an 18-2 advantage.
Warrington gave themselves a glimmer of hope with 15 minutes remaining when Dufty arrowed in from the left, Josh Thewlis's conversion reducing the arrears to 10.
But Wigan saw out the final moments with the minimum of fuss to take the trophy for the second time in three years and add it to the Grand Final, League Leaders' Shield and World Club Challenge trophies they already own.
"Enjoy tonight, enjoy this week, keep trying to get better - it never feels like we're done," Wigan head coach Peet told the BBC.
"I just like working with this lot. I love them to bits and I'm very proud of them.
"We don't worry about even the trophies, it's great but it's just another day to try and be our best."
He said it was "impossible" to give Burrow a fitting tribute.
"One try won't do it, one game won't do it," he said. "Our thoughts are with his family. I've never known a more respected man in this sport or any other."
