Galway manager Pádraic Joyce was "delighted" his side ground out a win in Omagh, although the victory was caveated by yet more injury concerns.
The westerners, without Damien Comer, Shane Walsh and Cillian McDaid, edged out Tyrone in a tense arm-wrestle, Cathal Sweeney's 49th minute goal proving decisive in a 1-10 to 0-12 triumph.
The win lifts Galway onto three points, with games against Derry, Monaghan, Dublin and Kerry yet to come.
"We're delighted to get out of here with two points. It probably wasn't the best game of football ever played," Joyce told Sunday Sport on RTÉ Radio 1.
"We started the game really well, went 4-2 up. Then we just seemed to run out of ideas up front, where we started carrying the ball into cul de sacs and didn't really penetrate Tyrone the way we should.
"In fairness to Mattie (Tierney) and Johnny Heaney, they got two great scores after half-time to bring it back to 6-6 because had that game gone 7-4, 8-4, there'd probably be only one winner.
"The impact we got off the bench from Danny Flaherty and Rory Cunningham was really good.
"The goal was probably the key turning point of the game, that gave us a big lift. Especially after missing two handy frees that Rob and Mattie should be scoring.
"We needed to regroup a bit (at half-time). There were a few harsh words said. These games, you can have all the skill in the world, and the tactical nuances of it, but unless you've heart and bottle and determination to go and win the game, that's what it boiled down to in the end. Thank God we showed enough of it."
Asked whether a defeat - and a one-point haul from three games ahead of a testing schedule - would have ratcheted up the pressure, Joyce replied: "There's always pressure. People in Galway expect an awful lot out of us, which is no harm. The lads probably hear more of it than I do.
"It wouldn't have been a disaster had we lost the game. But I think it might have been downbeat had we gone onto lose that game. It's definitely better to be going down the road with three points, besides one."
As if Galway's injury issues weren't extensive enough, they lost Paul Conroy at half-time, the midfielder emerging with a large bandage on his thigh, and Matthew Tierney also failed to see out the game.
Despite the perception that this had altered Galway's approach to the league, Joyce insisted that they hadn't gone "all out" for the 2023 league, notwithstanding their appearance in the decider.
"To be honest, we didn't actually go all out in the league last year. We actually stumbled into the final by default really. Because we had only one point out of two games as well last year.
"This year, we've just been absolutely hampered by injuries again. We've picked up two today with Paul and Mattie. It's definitely testing our squad depth and it's giving lads a lot of chances.
"These injured fellas that we have, some of them are a couple of weeks and a bit of long-term stuff. Normally we'd use the league to try and get football into them to get ready for championship. But they're going to miss out on the league a lot of them.
"So, it's not really a balancing act for us. It's trying to just get fit bodies on the pitch. At the moment we have 26 fit bodies and we're down two after today."
Tyrone boss Brian Dooher - on sole charge after Feargal Logan stepped away due to health issues - said he couldn't fault his team's workrate but that their decision-making had occasionally let them down.
"It's disappointing, a game we could and should have gotten something out of it - but we didn't. That's the long and the short of it," Dooher told RTÉ Sport.
"Just couldn't get a bit of momentum going in the second half at all and we were probably playing catch-up.
"In the second half, we just failed to get a grip on the game and we were probably playing second fiddle to Galway most of the time."
With two points from three, Tyrone are currently sixth in Division 1, ahead of Monaghan on score difference.
"We'll see what happens. I can't fault the boys for effort, they're working really hard. Things didn't drop their way today. Maybe some decisions, we'd do it differently the next time. By and large, their application and attitude, you couldn't question it. That's all we can ask for.
"Wherever that takes us, so be it."
Following their mid-week Sigerson triumph, neither Canavan brother played the entire game, Ruairí being pulled from the starting side beforehand and introduced in the second half, while Darragh was called ashore in the final quarter.
"Darragh and Ruairí, we could never question their commitment," said Dooher. "It was just a matter of looking after them. And balancing the training to make sure they could give their best for both of us.
"They obviously had their success with Sigerson. We congratulate them for it. Now we're glad to have them back for hopefully our undivided attention from now onwards."
