But Adkins' joy was tempered by the loss of inspirational midfielder Jem Karacan to what appears to be a long-term knee injury.
"It's a big result for us and Alfie [Le Fondre] does what he does so well," Adkins said.
"We're never going to get a later winner than that one. It's our third clean sheet in a row as well so were building momentum nicely.
"But it's a massive blow to lose Jem. It looks like he's going to be out for a long time, which is a shame. We've got our suspicions about it and it's fair to say that it's serious.
"He's been our stand-out player this season - he works so hard - and he's got a bright future ahead of him still. I'm sure he'll come back all the stronger."
Karacan was injured after he fouled Ross McCormack and fell awkwardly in the ninth minute.
Le Fondre's winner came after Stephen Warnock had fouled Le Fondre - and been sent off for a second yellow card - and Royston Drenthe fired over the free kick.
Danny Williams flicked it on and substitute Le Fondre pounced with a flicked header at the far post. He made a reputation for scoring from the bench in the Premier League last season, doing it eight times.
For Leeds manager Brian McDermott it was an unhappy homecoming on his first visit to the club, six months after the Berkshire club sacked him.
"That was tough to take tonight," he said. "I'm not sure why the referee was still playing. I've no idea.
"It was an awful feeling conceding so late but we did it to Brighton earlier in the season. But it won't define our season. We didn't deserve to lose that game but that's what Alfie does and he does it well.
"I'm gutted for the fans who travelled all this way. I've lost in play-off finals before [with Reading] and that was horrendous. It wasn't horrendous tonight but it was not nice and we move on."
McDermott - sacked by Reading in March after more than 12 years at the club, mostly as chief scout - received a warm welcome back from the Reading fans.
"I appreciated that a lot," he said. So, too, did Noel Hunt, the former Reading striker who moved to Elland Road during the summer.
Karacan's early blow rocked Reading. It was against Leeds, in April 2012, that Karacan had his Championship season prematurely ended due to a broken ankle.
He had endured heavy challenges from Danny Pugh and Michael Brown in Reading's 2-0 win and was taken off after the tackle by Brown.
Little was seen of a lightweight Leeds attack throughout, either from Hunt or Luke Varney. They did, though, have scant support from midfield or elsewhere.
When Varney did find space, he launched a weak effort at Alex McCarthy in the home goal.
Leeds could have won it deep into stoppage time from McCormack's free-kick but although Jason Pearce rose unmarked at the far post, he somehow nodded his effort wide.
It proved costly with Warnock conceding a free kick at the other end - "He should have stayed on his feet," McDermott said - and Le Fondre pouncing for the winner.