The damage was done in the first half as centre Jonny May pounced on a loose Joe Carlisle pass for the first try, with a conversion and four penalties from fly-half Tim Taylor putting the Cherry and Whites into a 19-3 half-time lead.
Replacement Freddie Burns added a further penalty and converted Tom Voyce's late try as Gloucester bounced back from their late defeat at Northampton last weekend.
Redpath is currently without 13 players through international commitments and injury, with scrum-half Dave Lewis, lock Alex Brown and wing James Simpson-Daniel all on the sick list today.
But a strong forward effort, with the back row of Peter Buxton, Andy Hazell and Matt Cox making a nuisance of themselves as the Warriors were outmuscled at the breakdown, and the accurate kicking of Taylor saw them punish a below-par Worcester.
Redpath said: "We were workmanlike, efficient and we were never under a huge amount of stress.
"We had 13 players unavailable and when you rock up the performance has to be workmanlike, it has to be protective in some format, as if you lose confidence during games like that you can crumble with inexperience.
"I am delighted with it, we were very efficient in what we did today and that was the pleasing thing.
"We knew Worcester were coming down saying they did not fear playing at Kingsholm, or playing this group of players, and we knew that would be a big driving force for us. The players have done Gloucester people proud today and deserved the win."
Redpath also hailed the performance of young lock Tom Savage, who marked his full Premiership debut with a tremendous display.
"He has gone from Hartpury thirds one year, to captaining Hartpury firsts the year after to playing in the Premiership," he said.
"He trained with us two pre-seasons ago as he was painting the halls and working in the bar and he asked if he could train with us.
"All credit to him and today was reward for all his hard work over the last two years.
"His performance was about doing the right thing: smashing people who ran into him and carrying ball. Forget about the tricks of the trade, just do what you do well rather than trying to exceed someone else. I am delighted for him."
Worcester boss Richard Hill acknowledged that his newly-promoted side, who grabbed a consolation try through Dale Rasmussen, had been some way off the pace as they came back down to earth after their win over Sale last weekend.
And he was particularly disappointed with his side's ill discipline, believing it had cost them a great chance to become the first visiting side to win at Gloucester in the Premiership since October 2009.
He said: "It was a poor show, we shot ourselves in the foot in the first half, going 19-3 down. We gave away penalties and an interception try and made too many unforced errors
"You won't get a better chance to beat Gloucester at Kingsholm, with the team they had there through unavailabilities and injury.
"Simpson-Daniel was a late pull-out, Alex Brown was injured. This was a great time to come here and take their record.
"We gave away a lot of silly penalties in the forwards, our defence is good and we need to trust our defence. I can't understand why we want to concede penalties when we don't need to do that."
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