Phil Dowson hailed Saints for the way they dug in the deliver another win at Welford Road.
The black, green and gold came back from 22-14 down during the second half to earn a bonus-point 31-22 Premiership Rugby Cup triumph.
David Ribbans doubled up during the first period to give Saints a 14-10 half-time lead, but Tigers then seemed to take control.
However, Fraser Dingwall set up Tom Collins and scored one of his own to put Saints 28-22 ahead, and James Grayson's penalty sealed the success.
It was a third successive win at Welford Road for Saints, who picked up their first victory of this campaign.
And forwards coach Dowson, who was in charge of Saints as part of Chris Boyd's coaching rotation programme during the cup, said: "It's unbelievable to win three in a row here because throughout my playing career, there weren't many happy memories.
"I'm delighted for the players who really dug in during the second half and came away with a really good win.
"We gave ourselves plenty of chances to win the game. We were wasteful in the first half five or 10 metres out, giving penalties away.
"We weren't necessarily as clinical as possible and if their kicker (Noel Reid) had a better day with the boot, the result could have been different.
"But we had some good combinations, we deserved the win and we created enough opportunities to win it."
Saints bossed the first half, aside from a sticky spell during the middle of it.
Noel Reid's missed kicks meant Tigers failed to build any real scoreboard pressure, until they went 22-14 up.
But Saints refused to relent and deservedly earned a win that means they can head to Saracens for next Saturday's Gallagher Premiership opener in high spirits.
"We started very well here," Dowson said.
"We spoke about starting strongly and trying to get stuck into Leicester.
"The backs put us on the front foot at times and the forwards got us some very good ball.
"In the first 10 minutes of the second half we gave a penalty away when we were right next to Leicester's sticks. If that was a score, maybe the complexion of the second half changes.
"But we then gave a ton of penalties away, we didn't get any rhythm in the game and Leicester are a good side who are on a bit of a momentum swing so there's going to be times when you're under pressure.
"But we weathered those, came through them and a lot of the talk was very positive to get back on the horse and get in the game."