Walder then pulled the deficit back to 16-13 with his second penalty shortly before half-time.
Varndell notched the third Wasps try after a good period of pressure, Walder's conversion again wayward.
Walder booted his third penalty of the afternoon to reduce the arrears to one point.
Fly-half Walder leaves after seven seasons while Italian prop Paoletti joined in 2005 from Plymouth Albion.
BBC: SPORT | Rugby Union | English | Newcastle axe Walder and Finegan
Dave Walder's boot pulled Wasps level at 30-30 with nine minutes remaining before Haughton's sensational winner.
Wasps scored through Paul Sackey, with Dave Walder converting, to make it 8-7 seconds before half-time.
When the visitors were penalised, Walder kicked a simple goal to seal the win.
Lamb was wide with a third-minute penalty, allowing Walder to give Wasps the lead three minutes later.
Two Davis penalties lifted the Chiefs, but a late place kick from Walder cemented the Wasps victory.
The visitors recovered from the early onslaught, Walder easing nerves with an 18th-minute penalty after an earlier miss.
That gave Irish an 18-13 lead, but Walder soon chipped three points off that with a third penalty.
After going in 3-0 down at the break, Wasps' six points came from Dave Walder's two second-half penalties.
Walder, 27, has made 93 competitive starts for the Falcons and has scored a total of 508 points.
BBC: SPORT | Rugby Union | English | Newcastle axe Walder and Finegan
Wasps mounted a sustained spell of pressure after the break but their only reward was a Walder penalty.
Olly Barkley was on target with two penalty attempts after the break but Walder's boot ensured Wasps' victory.
It is considered vital: Mr Walder describes it as the only scheme that will make a dent on overcrowding.
Walder and Lamb then both missed penalties before Jacobs ended a stunning move by smashing through four tackles to score.
The home side led 13-11 at the break as fly-half Dave Walder converted Ben Jacobs' try and kicked two penalties.
Walder levelled from 30 metres out and, after sustained pressure, gave Wasps the lead when the Chiefs conceded another penalty.
Cipriani was replaced by Dave Walder with 11 minutes left, leaving the field to a warm reception from the home support.
Bath pressure was converted into another three points 15 minutes later but Walder restored Wasps' five-point advantage with nine minutes remaining.
It was Walder's deft chip over the top that Varndell gathered to score on 33 minutes but his conversion drifted wide.
Even though Walder missed two penalties, he confidently struck the third in the 61st minute to reduce the deficit to seven points.
And the only second-half score was a penalty from Wasps' Dave Walder.
Walder converted, yet the home side remained firmly in contention when Taylor completed his penalty hat-trick before Fuimaono-Sapolu completed an impressive first-half revival.
Haskell's club colleagues Danny Cipriani, Tom Rees, Riki Flutey, Dominic Waldouck and Dave Walder have also yet to agree new contracts with Wasps.
The hosts' continual pressure resulted in five converted penalties from Walder's boot to draw them level at 30-30 with nine minutes to play.
Walder kicked Wasps into the lead with half an hour to play but they could not pull clear and Crichton made them pay.
Walder, who masterminded Wasps' fightback win against Leicester, opened the scoring with a 45-metre penalty before opposite number Taylor replied from much shorter range.
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.
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