The Rhinos produced a second-half resurgence as tries from Kevin Sinfield and Rob Burrow edged them ahead in the final minutes of a thrilling contest at the JJB Stadium.
Wigan's defensive grit and opportunism near the try line had seen them build what should have been a match -winning 16 point lead at half time, but Leeds' patience and application eventually saw them home.
"It was the most character shown by any team I've coached," said the Rhinos' Tony Smith.
And Leeds needed to show character because Wigan displayed plenty of their own, tackling tenaciously during the early stages when the Rhinos dominated possession.
The Warriors survived to take the lead against the run of play, Dennis Moran hoisting the high kick that was knocked back for substitute, Joel Tomkins, to score with his first touch."I was pleased with us in the first half," insisted Smith. "Apart from a seven or eight minute spell, I thought we were the better team.''
That spell, however, saw Wigan threaten to run riot. First, Wayne Godwin scrambled over then Tomkins's pass and Pat Richards's kick set up the impressive young full -back, Chris Ashton.
Leeds needed to score first in the second half and they did so when their influential replacement hooker, Shane Millard, spotted the Wigan defence dozing for once and darted over.
When he supplied the pass for Danny McGuire to skip past Harrison Hansen and Sinfield landed his second conversion, the Rhinos were only four points behind.Then, with perfect timing, Leeds hit the front with six minutes to go. Sinfield found the crucial play, dummying to pass and ghosting through before Burrow made it look easier than it had been by grabbing the Rhinos' fourth try.
The Wigan coach, Ian Millward, refused to be downcast despite starting the Super League season with two defeats. "We are a new team bedding in, but if we play like that every week I'll be one happy coach."
Wigan: Ashton, Calderwood, Richards, Vaealiki, Dallas, O'Loughlin, Moran, Logan, Higham, Palea'aesina, Hargreaves, Tickle, Hansen. Substitutes used: Brown, Seuseu, Godwin, Tomkins.
Leeds: Mathers, Donald, Walker, Senior, Smith, McGuire, Burrow, Bailey, Diskin, Peacock, Lauitiiti, Ellis, Sinfield. Substitutes used: Scruton, Poching, Jones-Buchanan, Millard.
Referee: R Silverwood (Mirfield).