Former Leicester Tigers forward Skivington was the driving force in an all-round dominant showing from the Exiles scrum that saw off the Cherry and Whites 18-12.
His two efforts, which came before the break, gave Irish a 15-6 half-time lead and despite Freddie Burns' best efforts - the England man kicking four penalties - they held on for their first win in any competition since November 11.
And Smith insists his troops can build on their Kingsholm success and put their poor recent form behind them.
"Winning at Kingsholm will give us a bit of momentum," said Smith. "We've got a few weeks now to freshen up some of the boys - then we'll load up for the big run home for the league.
"George [Skivington] was immense. He's stepped up in what's been a pretty tough season and led from the front.
"Both forward packs had a good crack at each other and it was won up front.
"It's a very different circumstance to when we came down here three weeks ago - we brought down kids, and it got a bit messy.
"They brought a big pack - particularly the back row - and we picked a big pack so we could go toe to toe with them. They put a lot of heat on the ball and it was tight, but we came out on top.
"The team showed a lot of character - we held out with our starting side as long as we could, and we just toughed it out.
"What pleased me most is the big W that'll be beside the result - I'm sick of seeing Ls."
After seeing his young Gloucester side lose two weeks running for the first time under his stewardship, director of rugby Nigel Davies urged his players to remember the disappointment, and to draw on it as they go forward.
The hosts had troubles at the scrum - shipping six points directly from scrummaging penalties - and Davies wants to see a reaction.
"We didn't turn up, emotionally we didn't turn up. You couple that with the error count and that's the reason we failed today," said Davies.
"I said to players, remember how this feels - because I don't want to feel like this again.
"We showed we're not good enough not to slip off the accuracy and intensity. We got it wrong, and it's not acceptable.
"You lose games in rugby, it's how you come back from that. We are still very much a work in progress.
"It's very difficult at scrum time. It's difficult for the referee, it's difficult for the players.
"It's a real mess at the moment. It can go either way, it really is a toss of a coin and it's truly frustrating.
"It's the same for everybody, but generally in the game there's a huge frustration in the scrum.
"We just need to get some momentum, and we've got some players coming back behind the scrum which will freshen it up a bit."
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