It sealed an extraordinary 3-3 draw with West Bromwich Albion at The Hawthorns.
Solskjaer's men had fought back to level after conceding two goals in the first nine minutes, only to seemingly see their hopes shattered when Baggies substitute Thievy Bifouma scored deep into added time.
But moments later Daehli turned and lashed home Wilfried Zaha's right-wing cross at the other end to send the travelling fans wild and leave stunned West Brom boss Pepe Mel still searching for his first home win.
Solskjaer, no stranger to late drama in his playing career, said: "It was very exciting but I think I've calmed down now.
"I'm so happy for the players and fans that we got the goal we deserved because we did not deserve to lose that game - absolutely no chance.
"We have had a couple of kicks in the teeth lately but we got the luck we don't feel we have had. We have deserved more points from the performances we have had and finally we got the other side of it."
But Solskjaer admitted his side had to learn from the torrid opening spell in which Morgan Amalfitano and Graeme Dorrans struck the Baggies in front.
A crucial relegation clash looked like turning into a nightmare for the visitors until Jordan Mutch reduced the deficit with a long-range effort Solskjaer conceded had been intended as a cross - then Steven Caulker back-headed a 73rd minute equaliser.
Solskjaer added: "We started really, really badly - I have never seen us so pedestrian. We might as well have just sat in with the fans, then maybe we would have woken up quicker.
"But the reaction was magnificent and it says it all about the team and the supporters who sucked the ball in for us."
Disappointed Mel questioned the time-keeping after fourth official Phil Dowd held up a board indicating four minutes of added time - only for Daehli to grab the equaliser one minute later.
Mel said: "I don't understand - four minutes are four minutes. Apparently an extra minute was played because we scored the goal, but there is no point talking to the referee because it can't be solved."
Mel's men looked home and dry after their dramatic opening spell and might have gone even further ahead but for fine saves from visiting keeper David Marshall to deny Matej Vydra and Youssouf Mulumbu.
But despite sliding deeper into the relegation dogfight, Mel insisted the circumstances of the result would not impinge on his side's survival prospects.
"We made the wrong decision when we were 3-2 up with 30 seconds to go, and that should have been the end of it," added the Spaniard.
"The changing room is quite bad but they will see tomorrow that we played a good game and the result should have been a better one for us.
"Simply by showing the players the video of the first half, and showing them how well they played, they will be able to see how capable they are of playing well."