The 19-year-old replacement fly-half slotted the crucial three-pointer with just over 10 minutes remaining after Gloucester had relinquished their hold on a West Country derby which they had largely bossed.
The Cherry and Whites had led 11-5 on a heavy pitch soaked after persistent rain, thanks to a try from outstanding prop Nick Wood and two Freddie Burns penalties.
Bath's try had come from wing Tom Biggs, and a penalty apiece from Olly Barkley and Tom Heathcote after the interval had levelled matters before Mills struck when Matt Banahan was guilty of not rolling away in the tackle.
Redpath praised the England Under-20 man, saying: "It's never an issue using Ryan in any big game.
"I was delighted for him, he has worked hard and today was a great reward.
"It was about giving him a chance and he kicked well, he had one great high ball and chase on Olly Barkley, and he had a great kick at goal."
Redpath also heaped praise on prop Wood, whose solid scrum presence and all-action showing in the loose made a mockery of England's decision to overlook his talents for their RBS 6 Nations squad.
"Nick was outstanding," he said. "His last two games have not been top notch, but outside of that over about 20-odd games, for him only to have two that haven't been up there is great. To finish off as he did today was good and his general enthusiasm was excellent."
The win, which completed a second consecutive league double over their nearest rivals and backed up last weekend's victory over Northampton, leaves Gloucester well-placed to mount a late surge for a place in the Aviva Premiership semi-finals.
But Redpath insists his side are not thinking that far ahead.
He said: "We are taking it one week at a time. We need to remain focused on what we can achieve from this massive run of games.
"We have Quins coming up at home and we definitely want a performance that gives us something against them, because we have played well against them on two occasions and come out on the wrong end of the result."
Defeat for Bath means they face an uphill struggle for a semi-final berth, and also dented their bid for Heineken Cup qualification.
Rugby director Sir Ian McGeechan felt a below-par kicking game had proved decisive in their reverse.
He said: "I think at 11-all we had the momentum but unfortunately we made a couple of poor decisions kicking the ball out.
"What we needed was a good clearance from the kick off but we didn't get it, they ran it back at us and we never really got back out of our half from there.
"Their kicking game was more astute than ours today."
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