Evans landed a penalty from wide out on the stroke of full-time to salvage a draw for the leaders after basement club Newcastle looked to be heading for a famous victory in front of their biggest crowd of the season.
Newcastle paid the price for ill-discipline with scrum half Chris Pilgrim sin-binned in the first half and hooker Rob Vickers - making his 100th appearance - yellow-carded in the closing quarter and the Falcons finished the game with 14 men.
It was no classic but it was a real scrap and Newcastle hustled their way into the lead in a fractious second half.
An interminable first half lasted 58 minutes with Quins hooker Chris Brooker treated on the pitch for a dislocated knee before being taken off on a stretcher.
There were several other stoppages and a sin-binning for Pilgrim after he pulled back Jordan Turner-Hall off the ball and the half ended with a scuffle between Falcons flanker Taiasina Tu'ifua, Turner Hall and his centre partner George Lowe.
Lowe reacted to a late hit from Tu'ifua and all three players were ordered down the tunnel by the match officials.
What little rugby that was played saw Evans kick a third-minute penalty and Jimmy Gopperth level the scores in the 11th minute.
Both kickers also hit the post while Gopperth was narrowly wide with a shot from halfway.
Newcastle would have been happy enough with a 3-3 scoreline at the break and possibly with the scores tied at 6-6 with 20 minutes left after Evans and Gopperth again exchanged penalties.
It was anyone's game and there was another scrap between Joe Marler and Ashley Wells after referee Andrew Small gave a penalty to Newcastle in the 66th minute and again Gopperth shaved the post from 40 metres.
Then Vickers was sinbinned for punching Marler with 10 minutes left - it could have been red - and it seemed a killer blow for Newcastle but within seconds Newcastle were awarded a penalty and Gopperth banged it over for a 9-6 lead.
It seemed Newcastle were on their way to a famous win but then up stepped Evans with his last-gasp equalising penalty.
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