After a physical start, Warriors were penalised at the breakdown and fly-half Oliver Bryant kicked his first penalty of the afternoon to give the visitors the advantage.
The home side instantly hit back with a penalty from Elliott Davies and, after a period of good pressure from Warriors, the fly-half added another to give his side a 6-3 lead.
This seemed to awaken Leicester and the visitors scored their first try of the afternoon when number eight Ed Milne went over the whitewash.
Davies added a further penalty before centre Henry Purdy scored a converted try for Tigers to give them a 15-9half-time lead.
The second-half saw Leicester dominate field position, which gave the hosts little opportunity to apply pressure, and they stretched their lead further thanks to two tries from replacement Jake Farnworth.
Bryant converted both tries and added a further penalty to give Tigers their second win of the campaign.
Despite the loss, Academy Manager Mark Hewitt will take heart from his side's defensive effort which, for long periods, protected their line against their physical opponents.
He said: "This was a very tough fixture against a bigger and more powerful side and I thought our players fronted up and matched them in most areas.
"Players can only tackle big men for so long before they start to fall off tackles so it was a big ask to win the game.
"I was pleased with the way we played when we had the ball and I'm sure the players will learn from this experience."
Hewitt's side face Gloucester Rugby this Saturday (12 January). The match kicks-off at 11am at Hartpury College and fans can watch for free.