Harlequins (23) 32
Tries: Care, Fa'asavalu Cons: Evans 2 Pens: Evans 5 Drop-goals: Evans Wasps (10) 22
Tries: Jewell, Lindsay, Haughton Cons: Walder 2 Drop-goals: Walder
Evans was capped 16 times by New Zealand
Nick Evans kicked 22 points to send Harlequins through to the semi-finals of the European Challenge Cup following a 32-22 victory over Wasps.
Danny Care and Maurice Fa'asavalu scored early tries for the home side.
Seb Jewell replied with a try for Wasps and Dave Walder kicked a drop-goal, before Evans kicked four sucessive penalties for Quins.
Wasps' Tom Lindsay and Richard Haughton scored second-half tries, while Evans added another penalty and a drop-goal.
The home side had a 14-point lead after only five minutes after convered tries from Care and Fa'asavalu, before Jewell's 12th-minute try got Wasps on the board, after a delay for the television official.
Walder kicked the conversion and then added a drop goal but Evans kicked three straight penalties before the break to give Harlequins a 13-point lead at half-time.
Evans continued his flawless display with his fourth kick seven minutes after the restart, Lindsay barrelled over for the try at the other end, before Evans scored his fifth and final penalty kick of the night.
Jewell and Mark van Gisbergen combined for Haughton to score Wasps' third try in the corner but Evans made sure he had the last say with a drop-goal four minutes from time.
In Friday's other quarter-final, Stade Francais beat Montpellier 32-28 in an all-French affair.
Harlequins boss Conor O'Shea:
"I would pay to watch Nick Evans train. [He] is genuinely a world-class player. We are very fortunate to have him here.
"We are very happy to be in the semi-final of a tough competition.
"You want to play at Thomand Park or in the south of France in the semi-finals of a massive competition. It is the place you want to be.
"We are glad to be the representatives from England in the semi-finals of this competition."
Wasps' stand-in director of rugby Leon Holden:
"The difference was losing three players before half-time, giving away two soft tries in five minutes and Nick Evans.
"Simon Shaw just spoke very well in the changing room... he also complemented the team on their performance.
"He said it was the best performance of the season."
Harlequins: Brown; Camacho, Lowe, Turner-Hall, Monye; Evans, Care; Jones, Gray, Andress; Kohn, Robson; Fa'asavalu, Skinner, Easter (capt).
Replacements: Brooker for Gray (48), Lambert for Andress (52), Vallejos for Kohn (56), Browne for Robson (78).
Not Used: Johnston, Moore, Clegg, William.
Wasps: Van Gisbergen; Haughton, Jacobs, Flutey, Lemi; Walder, Simpson; Payne, Webber, Broster; Shaw, Launchbury; Hart (capt), Ward-Smith, Powell.
Replacements: Wade for Lemi (21), Lindsay for Webber (32), Taulafo for Broster (60), Jones for Betsen Tchoua (67).
Not Used: Beech, Cannon, Davies, Mayhew.
Referee: Christophe Berdos (France).