Crichton had earlier on Saturday night scored his side's first try at Accor Stadium, but his 82nd-minute effort gave the Bulldogs their third win from the last four games.
That puts some oxygen into their September finals hopes after it was starting to look out of reach after losing five on the trot in April.
"It wasn't a very pretty win, but that's our style of game … it was a tight contest so it was awesome to get the result," Bulldogs coach Cameron Ciraldo said.
The Dogs and Sea Eagles gave their fans plenty of anxiety attacks in the final stages of regulation time.
Manly halfback Jamal Fogarty missed two field goal attempts, while Crichton missed his first and then baulked on the second as the defence rushed up in his face.
It had been a wrestle for most of the second half after the away side raced to an 8-0 lead, before Crichton's converted try had Canterbury trailing by two at the break.
Lachlan Galvin's sixth four-pointer of the season got the Bulldogs ahead for the first time in the match on 60 minutes, while Sea Eagles winger Lehi Hopoate's second of the night seven minutes later made it 12-12.
Kieran Foran's side had to dig deep after losing prop Kobe Hetherington (concussion) in the 10th minute and then hooker Brandon Wakeham (calf) just after halftime.
"I just thought we didn't execute at our best tonight," Foran said.
"The accumulation of error after poor error just kept them in the game and eventually it hurts you ... That's what those tight games are built on, moments."
If Crichton was trying to push for a return to the NSW Origin team, playing his first game at five-eighth for Canterbury seemed a strange way to do it.
"It's always been an option and he's shown some potential in that position," Ciraldo added of Crichton.
"The change was more around helping Burto (Matt Burton) find his best and most consistent form."
Manly back-rower Haumole Olakau'atu was up to his usual bullocking best, even though he nursed a left shoulder injury in the second half.
He still pulled off a try-saving tackle on Leo Thompson to underline his credentials for a return to the Blues' side for the July 8 decider at Suncorp Stadium - he was on the extended bench for game two at the MCG.
Sea Eagles fullback Tom Trbojevic gave his left hamstring a good workout in his return after nine weeks on the sidelines, running for 196 metres off 27 runs in an audition for a possible NSW recall.
"My focus hasn't really been on that … I haven't played footy in quite a while," he said.
The first half mostly belonged to Manly centre Reuben Garrick, who made a bust upfield in a 70m move which resulted in Hopoate's first try.
Then Garrick scored himself to reach 1414 points and pass Sea Eagles No.1 of the 1960s Bob Batty as the second-highest points scorer for the club - only behind club legend Graham Eadie.
