At jubilant Twickenham, the English club were better at the breakdown and ruthless on attack, while the Stormers' performance was riddled with soft errors.
Nick Kenningham went over in the eighth minute after the Stormers failed to protect the ball at ruck time, leading to a strong counter ruck and toe through from winger Nick David.
Two minutes later, a poor defensive read resulted in Cadan Murley going over in the corner and the Stormers found themselves 12-0 in as many minutes.
The domination continued at the breakdown and on the scoreboard as Harlequins No.8 Alex Dormbrandt received a beautiful inside ball to charge over from 20m out.
The hosts then secured the bonus point in the 25th minute after Kenningham charged down a box kick from scrumhalf Dewald Duvenage and Chandler Cunningham-South cleaned up to add another try.
The tries kept coming as David strolled over in the corner to put an exclamation point on a well-worked backline move. Marcus Smith added the extras and Harlequins were 33-0 up.
John Dobson’s men had a chance for a maul try from a lineout, but stout defence from the Quins thwarted their effort to keep them scoreless in the opening 40 minutes.
The Stomers started better in the second stanza, keeping the ball and playing in the right areas. But the hosts earned another turnover on their own line and went coast to coast to score their sixth try of the afternoon via David.
That man David scored his hat-trick after a wayward pass got an incredibly fortunate bounce to land in his hands and the winger cantered over from 30 metres out. The pain kept on coming as the diminutive Lucas Friday found space, chipped through and the bounce was never going anywhere but into a Quins hand and Zach Carr went over the whitewash.
The Stormers finally broke the dam wall in the 66th minute. Slick interplay out wide between captain Damian Willemse and Imad Khan saw the replacement scrumhalf score.
They found their rhythm late in the fixture, going all of 60m through a plethora of phases before winger Dylan Maart scored in the corner.
Jarrod Evans finally put the Stormers out of their misery with a ninth try in the last play of the game. The victory secures Harlequins a place in the last 16 of the Champions Cup.
Stormers coach John Dobson did not mince his words in summing up the Stormers' woeful performance in their 61-10 humbling at the hands of Harlequins in the Investec Champions Cup on Sunday.
Bulls Coach Johan Ackermann lamented the defensive efforts of his charges in their difficult 61-49 loss to Bristol Bears in the Champions Cup on Saturday.
The Bulls could not recover from conceding three tries in the opening nine minutes as the South African side went down 61-49 in their Champions Cup encounter against Bristol Bears at Loftus.
Stormers coach John Dobson has warned that a "desperate" Harlequins side could pose a serious threat ahead of Sunday's Investec Champions Cup clash at The Stoop.
