The Cherry and Whites were never behind in a pulsating match after fly-half Freddie Burns booted the first of his four penalties, although Quins threatened a comeback and finished the game at the end with a converted try to secure a losing bonus point.
Gloucester's young guns of wing Charlie Sharples and full-back Jonny May grabbed first-half tries, with May's a particularly good one after skirting three would-be tacklers and racing home from 45 metres.
Flanker Akapusi Qera rounded off a well-worked backs move in the second half that numbed any threats of a Quins fightback after full-back Ross Chisholm scored the first of his two tries - the other coming at the end - and Kiwi fly-half Nick Evans landed 13 points.
The downside to Gloucester's performance was that they failed to get the four-try bonus point which seemed in their grasp as Quins were pinned back in their own half as the game wound down to its conclusion.
Redpath said: "There has been a lot of criticism about the Premiership, and, in parts, rightly so, over the past months but this was good and a great opportunity for us to get the bonus point.
"It was crucial, as it was for them, but it was a great advert for the Premiership and excites the crowd.
"But we have won nothing yet and achieved nothing yet. I don't think that is something to get too excited about. We blew an opportunity."
He especially marked out former England international wing James Simpson-Daniel, who set up Sharples' try and nearly scored one himself.
Redpath added: "I thought James was exceptional. He did hardly anything wrong in the whole game and when you talk about the young kids and what people do and don't do well, you will see that James has a high percentage of things that go well. That comes with experience.
"I'm delighted for all the players. It was a really great game and now we must strive for that top four in the league and we have six games left which are huge."
Redpath also dismissed claims from Quins director of rugby Conor O'Shea that a crucial drive on the Gloucester line in the second half should have been awarded as a penalty and Qera should have been sin-binned.
O'Shea said: "That was a penalty to us. Qera just ripped the ball off the ground, off his feet. It is then a one-score game with 15 minutes to go but that is the way it is.
"Sometimes those go for you and sometimes they go against you. Sometimes it's a sin-bin it was a straight penalty if not a yellow card. With minutes to go, it would have been interesting but it knocked the stuffing out of us.
"However, take nothing away from the game. For a neutral, that was great. At the end of the day, they took more chances than we did.
"We had loads of opportunities and it was two teams who went toe-to-toe."
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