Inspired by their expensive newcomer, Leeds had fought back impressively during a thrilling second half, only to be robbed of the draw that was the least they deserved by Farrell's boot and cool head.
The Wigan coach, Eric Hughes, has had much to say over the last, uncomfortable couple of weeks, about the lack of bulk and power which he has at his disposal, but an unlikely looking forward pack performed well enough for him in the early stages at Headingley.
After two penalties from Farrell had outweighed one from Leeds' Graham Holroyd, Wigan's French second-rower, Gael Tallec, had what would have been a splendidly inventive try disallowed when he failed to touch down after taking his own kick on the bounce and heading for the try-line.
There was an argument as well about the try that was allowed, but Jason Robinson had come from a marginally onside position to scoop up Farrell's grubber kick and send the supporting Craig Murdock over the line, Farrell adding the conversion.
After 32 minutes during which they had posed few problems for Wigan's defence, Leeds brought on their record signing. Virtually Harris's first act was to wrong-foot Terry O'Connor and Tony Smith with a little shimmy and send Phil Hassan in for a try. Just to embellish his dream start, Harris, taking over as kicker from Holroyd, the man he had replaced, added the conversion.
Harris continued to be heavily involved for a player who had only had two training sessions with his new team-mates, with Richie Blackmore in particular enjoying a service which promised to unlock his match-winning potential.
Wigan were starting to look worryingly scrappy before a little glimpse of guile from Farrell steadied their nerves. The Wigan captain dummied to kick, which gave him enough space to send Gary Connolly through a gap. Robinson backed up to score, although Connolly's final pass looked suspiciously forward.
Leeds should have hit back when Adrian Morley made as good a break as any second-rower in the game could produce. That chance was wasted but Holroyd, back on the field, soon put over a penalty.
Harris and Holroyd then linked up to send Hassan, originally from Wigan, in for his second try, Holroyd landing a fine kick to bring the scores level with 13 minutes left.
Leeds could have won it when Martin Masella made a marvellous run but failed to find the supporting Damian Gibson and again when Harris's cross kick picked out Paul Sterling, who was stopped two yards short by Connolly.
Cruelly, with two minutes remaining, Farrell gathered a low pass from Martin Hall, steadied himself and slotted over the winning point.
Leeds: Gibson; Sterling, Blackmore, Hassan, Rivett; Holroyd, Sheridan; Masella, Collins, Mathiou, Morley, Anthony Farrell, Mercer. Substitutes used: Harris, Hughes, Newton, Leathem.
Wigan: Murray; Robinson, Connolly, Radlinski, Johnson; Smith, Murdock; O'Connor, Cassidy, Holgate, Haughton, Tallec, Andy Farrell. Substitutes used: Hall, Baynes.
Referee: S Cummings (Widnes).Reuse content