The Jags, looking for their first home league win of the season, were the best team in the first half but striker Kris Doolan missed a great chance in the 39th minute when he headed over from close range.
Doolan missed a better opportunity in the 51st minute when he failed to beat Easter Road goalkeeper and captain Ben Williams after he was clear on goal.
Hibs all but failed to test Thistle keeper Scott Fox at all until Craig curled a wonderful shot past him in the 68th minute.
Fenlon said: "It was a bit of smash and grab from us if I'm totally honest.
"I thought Thistle were excellent in the first half and played really well but they probably had more chances in the second half.
"We were a little bit better in the second half and played better once we scored.
"I'm delighted with the three points as it's a difficult place to come.
"They're a real good side, with a good system and they pass the ball really well.
"They had a lot of possession in the first half but didn't cause us loads of problems in front of goal but they created three or four in the second half and Ben made some terrific saves."
Indeed, the Irishman was glad to see Williams back to his best after conceding three goals at Inverness last week.
He said: "Ben has been a fantastic keeper for the club since he's been here.
"His game temperament is fantastic and I knew last week wouldn't bother him. He's that type of character who just gets on with it."
On Craig's sixth goal of the season, Fenlon said: "We've been told Liam Craig can't play on the left for us but he still chips in with goals.
"It was a great goal with his right foot - a fantastic finish - and it was difficult because it was bouncing, it wasn't on the ground, but he controlled it and put it away in the top corner."
Thistle manager Alan Archibald must have thought he was watching a familiar movie as his side passed up several chances before succumbing to Craig's winner.
He said: "It was a sore one to take. I thought we played a lot of good stuff and created a number of chances.
"What was missing was a clean sheet, at least you take a point from that, that was the disappointing thing.
"We haven't kept a clean sheet since the first game of the season and if you don't keep clean sheets you don't win games, it's a simple as that.
"It is frustrating obviously but it would be more frustrating if we weren't creating any chances and we were playing really poor football.
"But we are playing good football and we are knocking it about well.
"I said that to the players there, it would be easier if we had been terrible tonight.
"I could have come in and had a go at them, and read the riot act but it wasn't the case."