The two teams clash at Welford Road in Round 6 in what should be the defining game in the pool. Ulster host Montpellier in the next round in the new year, while Tigers have to go to Benetton Treviso.
"I'm delighted for the players, it's their victory. We hadn't won in France since 2006 and so this group of players have made a little bit of history for themselves," said a delighted director of rugby, Richard Cockerill.
"It was a massive win and potentially the defining moment that can get us out of the pool. This puts us in good position to finish top of the group, and maybe get a home quarter-final, although there is still a long way to go and we can't take Treviso lightly.
"But it's still in our hands and this was what we needed in the competition because the four points will keep the pressure on Ulster.
"This is massive for us, with another massive game in Treviso to come. We can't take anything for granted but we want to get the win there and then bring Ulster to Welford Road for a grand stand finish.
"At 14-8 we could have been happy to take the bonus point and not risk losing it but, credit to the players, they kept playing and manufacturing opportunities to score tries even if we didn't necessarily take them."
The last Tigers win in France had been in a pool game in Bourgoin in 2006, 28-13, but since then they had lost seven straight matches on the other side of the channel.