Warrington did a good job of containing Harris, back at Wilderspool for the first time since his record transfer, but his five goals from as many attempts proved the difference between the sides.
Warrington had a great chance to go ahead before Leeds scored their first try, but Richard Henare hung on instead of passing to the unmarked John Roper.
Leeds soon punished them, a combination of Harris's pass and poor tackling from Paul Sculthorpe and Lee Penny putting Ryan Sheridan in.
Salesi Finau squandered the next inviting opportunity for Warrington, throwing a wild pass after running into the clear. They finally registered their first points when Lee Briers spotted a gap and made a diagonal dash to the line.
But Leeds, making more of the openings they created, went back in front, Wayne Collins burrowing over from dummy half for Harris to add his second goal.
Roper took Briers's pass to go in immediately before half time, but Briers's missed conversion left Leeds narrowly in the lead at the break.
The lead did not last long. Leroy Rivett knocked on to get Warrington possession from a scrum as Briers's perfectly weighted kick sat up neatly for Mark Forster. Forster was soon the hero at the other end, stopping the captain, Marvin Golden, after Harris and Adrian Morley had sent him racing for the line.
It was all to no avail, though, because Leeds moved the ball left to score through Phil Hassan. Harris, who had earlier kept Leeds in contact with a penalty, landed his fourth goal from the touchline.
Warrington had their chances in the time remaining, notably when Henare lobbed the ball over the line, but Harris's boot clinched it when Mike Wainwright was penalised for holding down, and Graham Holroyd tagged on a last-minute drop goal.
Warrington: Penny, Henare, Finau, Roper, Forster, Wainwright, Briers, Chambers, Swann, Hilton, Eyres, Tatupu, Sculthorpe. Substitutes used: Duffey, Stevens, Mann, Knott.
Leeds: Holroyd, Sterling, Gibson, Hassan, Golden, Harris, Sheridan, Masella, Collins, Mathiou, Hay, Farrell, Mercer. Substitutes used: Rivett, Morley, Newton, Field.
Referee: S Ganson (St Helens).Reuse content