George Lowe touched down for Harlequins' fifth try and replacement fly-half Ben Botica marked his Aviva Premiership debut with a late score off the bench, while Nick Evans kicked 10 points.
After the fireworks of Harlequins' Premiership record comeback victory over Wasps at Twickenham last week, this was a far more routine win for the reigning champions.
London Welsh, who managed a sole penalty from fly-half Gordon Ross, have had a brutal introduction to the demands of the Premiership.
Quins were forced to stage the game on a Friday night because Lady Gaga is taking up a two-night residency at Twickenham, just over the A316, this weekend.
That was particularly tough on Premiership new-boys London Welsh, who were forced to face Harlequins just five days after their top flight debut against Leicester.
By the time they got close to the pace of the match, Harlequins had surged into a 21-3 lead with two tries from Monye after Robson had crashed over in the fifth minute.
Harlequins had an extra day to recover from their sensational 42-40 comeback win against Wasps last Saturday and started like an express train.
Evans, the architect of Harlequins' record turnaround at Twickenham, chipped in behind the London Welsh defence for Lowe who slipped the pass to Jordan Turner-Hall.
Mike Brown was screaming for the ball on the outside but Turner-Hall kept hold of it, Quins recycled and Robson scored from close range to get Harlequins off to a perfect start.
Four minutes later, Harlequins were in again. Tom Guest's charge splintered the London Welsh defence but turned the wrong way and again missed the chance to send Brown screaching away.
London Welsh conceded a kickable penalty but Harlequins went for touch and built the pressure from the lineout and Evans spun a long pass out to Monye for the try.
The Exiles temporarily halted the one-way traffic with a ferocious tackle from centre Hudson Tong'uiha on Monye to win a penalty and edge into Harlequins territory.
Full-back Tom Arscott then cut a sensational line through a clutch of players and when Harlequins were penalised for offside, Gordon Ross kicked London Welsh on to the scoreboard.
The respite was temporary for London Welsh. Joe Ajuwa made a hash of a high ball and Monye pounced, setting another Quins attack in motion before receiving it back for another simple finish.
Ross turned down the chance of a second shot at goal but London Welsh lost the lineout and went into the break trailing by 18 points.
After a flat 20 minutes, Quins upped the tempo straight after the interval with a powerful carry from Chris Robshaw into the London Welsh 22.
London Welsh prop Paulica Ion was sin-binned for preventing a quick tap penalty and Harlequins almost profited immediately.
Evans spread the ball wide from the five-metre scrum but Brown was closed down quickly and could not quite squeeze the scoring pass to Tom Williams.
Harlequins kept the pressure on and did take advantage of London Welsh being short-handed with Robson scoring his second try of the evening from close range to earn the try bonus point.
Conor O'Shea began to ring the changes, sending Danny Care on for Karl Dickson and Nick Easter for Guest.
Having been relegated to the bench, Care had a point to prove in front of the watching England coach Stuart Lancaster and one audacious back-of-the-hand pass sent Monye away.
Brown launched another attack from deep and was taken out off the ball after chipping ahead but referee Luke Pearce waved play on and Lowe followed it up to score.
Evans landed his fifth conversion of the evening before making way for Botica, the son of former Wigan and New Zealand rugby league player Frano, who rounded off a comfortable Harlequins win with a late try.
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