Harlequins had not won their opening three games of a season since 2003
Harlequins continued their fabulous start to the season with a bonus-point thrashing of toothless Gloucester.
Freddie Burns gave the visitors a brief lead which was cancelled out by winger Sam Smith's score in the corner and young Luke Wallace's pushover try.
Burns landed a long-range penalty before Nick Evans extended Quins' lead on the stroke of half time.
Ugo Monye crossed for his third try of the season before Wallace claimed his second and Brooker made it five.
Gloucester started well in slippery conditions at a rain-soaked Stoop when a chip kick resulted in Burns's shot at goal in front of the posts.
Evans was again instrumental in orchestrating Quins going forward and, after he fashioned a chance for Mike Brown which went begging, it was his blindside break that resulted in Smith's try, after some fantastic hands from George Lowe.
Evans converted and shortly after elected to go for the corner rather than the posts.
The decision led to a dynamic maul that saw the impressive Wallace emerge with the ball over Gloucester's line.
The two fly-halves exchanged penalties before the break but 10 minutes into the second half the going got worse for the Cherry and Whites when openside Matt Cox was sin-binned.
Evans produced a blistering line break from quick line-out ball that took the hosts to within 10 metres, and, when the ball was recycled with pace, Quins utilised an overlap to put Monye away for his third try in three games.
Harlequins' pack dominated their opponents to earn Wallace his brace and a bonus point.
Evans was again on target before he was substituted for Rory Clegg who quickly landed a penalty.
With five minutes remaining replacement hooker Brooker burst through to score and Clegg made it a seven-point score.
Harlequins director of rugby Conor O'Shea:
"It's not about winning the game today, it's about the next minute of the next game. So we are not getting carried away at all because this is a marathon.
"We are comfortable with the way we are trying to play, the shape we have, the intensity we have.
"But we know that in the next minute of the next game, if we don't approach it with the intensity and physicality we need to, we will be blasted, and that's not going to happen.
"This is the standard we want to set. You're as good as your next game, not your last one."
Gloucester head coach Bryan Redpath told BBC Gloucestershire:
"It was embarrassing. Our basics and discipline were poor, we didn't get enough control or set piece possesion.
"The players need to look in the mirror and see what that performance was, because it was unacceptable.
"We didn't get a stranglehold on the game outside of the first 10 minutes."
Replacements: Walker for Lowe (69), Clegg for Evans (61), Bolt for Dickson (64), Marfo for Lambert (76), Brooker for Gray (64), Sinckler for Fairbrother (76), Matthews for Robson (69), Trayfoot for Robshaw (69).
Replacements: May for Trinder (72), Robson for Runciman (63), Murphy for Wood (69), Dawidiuk for Charles (50), Chistolini for Harden (57), Lyons for Brown (71), Evans for Deacon (67).
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