Leeds (3) 8
Try: Burrell Pen: Thomas
Wasps (7) 17
Tries: Simpson, Rees Cons: van Gisbergen 2 Robinson Pens: van Gisbergen
Simpson set Wasps on their way with the opening try
Wasps piled on the misery for Leeds by inflicting a seventh successive Premiership loss on the bottom club.
Joe Simpson livened up a lacklustre opening half with a wonderful try just before the break to help the visitors to a nervy 7-3 lead.
Flanker Tom Rees burrowed over for a second five-point score shortly after the restart to stretch the lead.
And although the hosts hit back through Luther Burrell's try, they rarely threatened to complete the comeback.
A struggling Wasps side, who had been hammered 37-10 by Northampton last weekend, looked as though they could provide Leeds with a good chance of ending their disastrous start to the season.
But the hosts created precious little against an under-strength Wasps who were missing Simon Shaw, Dave Walder, Ben Jacobs, Rikki Flutey and Richard Haughton.
They struggled to threaten the try-line and instead looked to their forwards to bulldoze their way through the middle.
A tepid first 35 minutes finally came to life when Wasps resisted some Leeds pressure to score as Simpson took the ball from the back of a scrum and raced from inside his own half to cross the line.
His superb effort was comfortably converted by Mark van Gisbergen before Ceiron Thomas slotted a penalty for the hosts just before the interval.
Six minutes after the restart, Wasps grabbed a second try when Simpson's short offload found Rees and he piled over from close range and Van Gisbergen converted before missing a penalty.
Leeds responded when Scott Mathie and Henry Fa'afili combined to tee up Burrell who ran clear.
Thomas hit the post with his conversion and a van Gisbergen penalty settled the away side's nerves as they held on despite a late Leeds pressure.
Leeds director of rugby Andy Key:
"We had little to show for all our possession and that's probably come down to a lot of unforced errors and mistakes at crucial times.
"It really is difficult to put our finger on why these things are happening, because they have to change if we are to get our first win.
"We fancied our chances massively today but we also knew Wasps were coming off the back of a bad defeat against Northampton.
"We knew that they would be coming here to compete hard and you could see that at the breakdown."
Wasps director of rugby Tony Hanks:
"Wasps don't lose games like that last week [at home to Northampton] and emotionally it took a lot out of us.
"The guys have taken a bit of a battering but they are their own biggest critics. They've looked at themselves in the mirror and thought 'we need to be better than that as a team'.
"I'm pleased with the way we responded but it has to be a stepping stone towards greater consistency."
Leeds: Thomas; Stephenson, Burrell, S. Barrow, Fa'afili; MacKay, Mathie; Hardy, Titterrell, Gomez, T. Denton, Wentzel, Myall, Oakley, Browne.
Replacements: Hinton for Thomas (63), Blackett for S. Barrow (28), Fury for Mathie (57), Alonso for Hardy (48), Swainston for Gomez (61), Paul for T. Denton (48), To'oala for Browne (61).
Not Used: Nilsen.
Wasps: Wallace; Varndell, Waldouck, Kefu, Lemi; van Gisbergen, Simpson; Payne, Ward, Broster, Veale, Ward-Smith, Worsley, Rees, Powell.
Replacements: Taulafo for Ward (57), Hobson for Broster (48).
Not Used: Webber, Cannon, Betsen Tchoua, Berry, Jewell, Daly.
Ref: Dean Richards (RFU).