Nick Selman scored an unbeaten 116 as Glamorgan chased down a target of 266 in 51 overs to beat Durham by three wickets with three balls to spare.
The match was Hogan's first as skipper following Jacques Rudolph's decision to step down from the four-day captaincy.
"It got a bit tense at times, but I felt we always just hung on to that possibility of winning," Hogan said.
"We thought about shutting [the chase] down, but the boys came in, kept us in it and we were lucky enough to win it."
Glamorgan benefitted from an attacking declaration by Durham captain and former England all-rounder Paul Collingwood, after a rain delay.
The 21-year-old Selman batted through the innings before hitting 14 off the first three balls of the final over.
"He's probably the grafter of the team, the guy we look to to face a lot of balls and I didn't think he had it in him," Hogan joked.
"I've never seen him hit a six in my life, but he's come off when we needed him, he's played really well."
Brisbane-born Selman is in his second season with Glamorgan after time in Queensland's age group sides and the Kent second XI.
He scored his maiden century at St Helen's in 2016.
Hogan said he'd enjoyed his first match in charge of the team after Rudolph's decision, and didn't rule out continuing in the role next season if asked.
"If things go well I'd like to do it, it's up to the club as well," he said.
"But at this period of time it's just until the end of the season. We'll see then whether I'm happy and the club's happy, it's easy to say after a win but so far I'm enjoying it."
Glamorgan's next game is at Worcester on Friday 9 June after sitting out a round of Championship matches.
Glamorgan captain Michael Hogan praised his team's batting performance in their first Championship win of the season.