Lima had scored just once in his first 26 matches for the Warriors but he doubled his tally on 24 minutes and, after the Rhinos had threatened to pull off the biggest comeback in Challenge Cup final history, he struck again just past the hour mark to keep his side on top.
It was enough to earn the front-row forward the Lance Todd Trophy as man of the match.
Another Kiwi, hooker Thomas Leuluai, finally ended Leeds’ brave fightback and made sure of Wigan’s record extending 18th Cup success when he forced his way over for a fifth try three minutes from the end.
It was the Rhinos’ second successive Wembley defeat and their fifth Cup final reverse since they last experienced victory in 1999 but, unlike last year against Warrington, this time they went down valiantly.
At one time they trailed by just two points, having matched Wigan’s four tries, but captain Kevin Sinfield was able to add only one conversion and for a time his misses looked crucial.
However, there was little hint of the drama to come when the Super League champions justified their pre-match favouritism by racing into a 16-0 lead after 27 minutes of virtually flawless rugby that thrilled the 30,000 Wigan fans among the 78,482 crowd.
The warning signs were there in the first minute when Brett Finch got second rower Ryan Hoffman breaking out of his own half and it was no surprise when Sam Tomkins combined with brother Joel to create the opportunity for right winger Josh Charnley to open the scoring after nine minutes.
Leeds scrambled to halt the ever-dangerous Sam Tomkins as they struggled to get a foothold in the game.
Wigan made the most of a fumble by full-back Brent Webb, with replacement Paul Prescott getting Lima romping through a gap for only his first try.
Richards added the conversion and it was quickly 16-0 when Joel Tomkins scored what will go down as one of the greatest tries in Challenge Cup final history.
Inevitably, Sam Tomkins was at the heart of the move, stretching the Leeds defence out of position with a weaving sideways run before releasing his older brother.
Joel Tomkins saw clear space after handing off Leeds half-back Danny McGuire and he had the pace to hold off the cover to finish off in spectacular fashion for an 80-metre try.
It was in danger of becoming a rout but the Rhinos hauled themselves back into the game with two quick-fire tries just before the break.
First captain Kevin Sinfield took a return pass from Jamie Jones-Buchanan and combined with McGuire and Carl Ablett to get winger Ryan Hall over for the 100th try of his career.
Sinfield saw his conversion rebound off an upright but he was on target from the touchline three minutes later after the impressive Ben Jones-Bishop had produced a superb finish following good approach work from Rob Burrow and Watkins.
Leeds were rejuvenated by their scoring burst while uncharacteristic handling errors from Sam Tomkins, Michael McIlorum and Prescott in the first five minutes of the second half suggested Wigan were suddenly looking vulnerable.
Rob Burrow came more into the game for the Rhinos and Hall produced a couple of storming runs as the Yorkshiremen began to play the game in their opponents’ half.
Another knock-on, this time from Hoffman, enabled Leeds to maintain the pressure and it paid off on 58 minutes when centre Ablett crashed over for his side’s third try.
Sinfield was wide with the conversion attempt but the gap was down to just two points as the game entered the final quarter.
Leeds were on course to break the record for the biggest comeback in Cup final history, St Helens’ successful overturning of a 14-point deficit against Bradford in 1997.
But Wigan’s response to the growing crisis was swift and decisive as they worked their way up field to set up the position for Lima to score his second try.
Lee Mossop’s short pass looked suspiciously forward but the big Kiwi took his chance superbly, fending off the attempted tackle of Ablett to rumble over from 10 metres out.
Richards’ third goal made it 22-14 but there was another twist on 71 minutes when Hall forced his way over at the corner for his second try, his 99th for the club.
Sinfield was wide with the goal kick, leaving him with just one success from four attempts.
Leeds had one more chance to snatch it when the impressive Jones-Bishop rounded Richards and kicked ahead for McGuire but Sam Tomkins just did enough to remove the danger and Wigan made sure when hooker Thomas Leuluai forced his way over for a fifth try three minutes from the end.