Two penalties in the space of two minutes from Robinson increased the home side's lead even further, before Wade's second try on 12 minutes opened up a solid lead.
Another penalty from Robinson, before Wade's third try of the game, gave Wasps a further advantage after 25 minutes played.
Two penalties from Evans on 30 and 34 minutes brought Harlequins back into the game.
The half-time whistle blew with the Wasps holding a 28-13 lead.
A try from Tim Payne on 56 minutes saw Wasps increase their lead further as they looked to capitalise on a good first half.
However, a try from Tom Guest and two from Mike Brown brought Harlequins back into the game.
Nick Evans's conversions ensured that a fightback was on as the away side sensed a chance to take control of the game.
On 68 minutes, Evans scored a try to bring his side closer to drawing the scores level.
Two minutes from time, Evans got the important drop goal to put Harlequins in the lead for the first time in the game.
The full-time whistle blew with the scores at 40-42 after an impressive second-half comeback from Harlequins.