In front of an 8,000-plus crowd, the Falcons made hard work of it against a Quins side that came close to winning the match in injury time.
Wallaby star Matt Burke, making his home debut, clattered through on his first touch to set the ball up perfectly, but it was the drive of Stuart Grimes and Michael Stephenson who forced a second minute penalty which Wilkinson missed narrowly.
He missed again in the sixth minute when Mike McCarthy and Stephenson got on the end of a Jamie Noon break and Andre Vos was over the ball and lucky to avoid the Sinn – they were two uncharacteristic errors even in the blustery wind.
Quins got away with a series of penalties without more than a few words from the referee and Newcastle lost Mark Mayerhofler after 15 minutes with a leg injury as Wilkinson finally got it right with a penalty to make it 3-0.
Quins swept into the lead when Jeremy Staunton kicked a penalty and Gavin Duffy broke through two tackles and passed inside for George Harder to score. Staunton's conversion made it 10-3 against the run of play.
Newcastle were finding it hard to make headway in midfield with Quins up quick and playing it right on the margin for offside but they were caught in the 28th minute and Wilkinson made it 10-6 and then McCarthy was lucky to escape the sin-bin when he went over the ball and Staunton kicked the penalty.
Luke Sherriff was finally sin-binned in first half injury time after enormous Falcons pressure and Wilkinson made it 13-9 with the penalty.
But straight from the restart, Newcastle's midfield defence was awful and Staunton sailed through and Gavin Duffy scored easily.
Newcastle mounted a furious riposte with three line-out drives and Colin Charvis was held up over the line.
Simon Miall was sin-binned in the 51st minute for persistent offside and Wilkinson made it 18-12 with the penalty.
Wilkinson spurned a kick at goal to find touch in the corner and Newcastle battered away at the line with Charvis, Peel and Gross close.
And, when Quins killed the ball as Gross went for the try, referee Sean Davey gave a penalty try and Wilkinson's conversion put Newcastle 19-18 in front.
The home side had the squeeze on in the scrum and a penalty for taking it down saw Wilkinson kick his fifth penalty in the 71st minute.
Neil McCarthy was sinbinned in the 74th minute for not rolling away in the tackle.
That put Newcastle under severe pressure and Staunton reduced the lead to just one point with a penalty in the 78th minute.
Staunton had the chance to win it for Quins in the fifth minute of injury time with another penalty but he pushed it wide.
For Newcastle Falcons:Try: penalty tryCon: Wilkinson Pens: Wilkinson 5
For NEC Harlequins:Tries: Harder, DuffyCons: Staunton Pens: Staunton 3
Yellow card: Sherriff (Newcastle Falcons, 40)