The visitors had plenty of possession and were only 19-10 behind when Quins had Luke Northmore and Danny Care sin-binned for cynical offences, but they couldn’t take advantage.
Instead, Tabai Matson’s men confirmed the victory and the bonus-point when back to 15 men as Cadan Murley went over to complete his brace.
Huw Jones and Louis Lynagh also touched down for the hosts, with Tommy Allan kicking two conversions, while Tom Marshall and Will Haydon-Wood’s penalty provided the Falcons’ response.
Saracens do have the chance to regain their spot in second when they face Leicester Tigers on Saturday, but Quins are in a good position heading into the latter stages of the Premiership campaign.
Harlequins opened the scoring in the fifth minute when fly-half Allan made a superb break from halfway that took him towards the left wing, with his pass inside giving Jones an easy run-in.
Allan added the conversion for good measure, with the hosts going on to comfortably repel Newcastle’s attempt at responding to their early setback.
The Falcons turned down the chance to get on the board with a simple penalty from in front of the posts and quickly rued that decision when George McGuigan knocked on after tapping and going.
It was a decision they did not repeat, as Haydon-Wood did get them off the mark after another penalty from short range was awarded.
Having had little of the ball for around 15 minutes, Quins reasserted themselves just before the half-hour when Care received possession out of a driving maul before his pass allowed Murley to burst over the line.
Try number three for the hosts arrived in the 32nd minute as Tyrone Green received Andre Esterhuizen’s pass before using his pace down the right and putting Lynagh in the clear.
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