Cooney scored two superb tries, denied Quins a certain score with his covering defence early in the second half and kicked three conversions and a penalty.

Luke Marshall, Matt Faddes and Tom O’Toole also crossed for the visitors, with Ulster making it four wins from four and setting up a pool-deciding trip to Clermont Auvergne in round five.

Quins, whose slim qualification hopes ended, will undoubtedly be sick of the sight of Cooney, who picked up right where he left off last week by booting a seventh-minute offside penalty.

Ulster dominated the opening quarter in both possession and territory without finding a telling score, although the irrepressible Marcell Coetzee came closest with a barrelling break down the left flank.

Aside from occasional glimpses of the running rugby they are capable of – Cadan Murley making a determined charge out of his own 22 – Quins did not have their first attack until after the half-hour mark.

Stephan Lewies appeared to have spurned the initial chance by knocking on in the tackle following a line break but a few phases later Travis Ismaiel almost went over in the corner, before settling for a James Lang penalty.

However, Ulster led 10-3 at the break thanks to a scintillating length-of-the-field try.

Billy Burns made the initial break, handing-off a defender and offloading to a streaking Jacob Stockdale, before Cooney completed the score by sliding over following Faddes’ pass inside.

Early in the second half, Quins almost replicated that but Ross Chisholm was hauled down by Cooney five metres short after a brilliant 40-metre break by Semi Kunatani.

And Ulster increased the hosts’ frustration shortly after by getting their second try, when Marshall collected Stuart McCloskey’s clever grubber through and powered over the line.

The game began to get out of hand for Quins as Cooney kicked through from the base of a ruck, gathered the ball and touched down for try number three on the hour mark, with his third conversion making it 24-3.

Powerful lock Lewies did burrow over from close range shortly after to give the home fans some joy but Ulster capitalised on an overthrown Quins lineout to seal the bonus point late on.

Faddes made the most of an overlap to power over in the right corner after that set-piece mistake and there was even time for a fifth Ulster try as O’Toole dotted down with the final play.