Academy graduate Conway received a nice weighted through ball from Han-Noah Massengo and was able to finish from close range.
The forward has already scored for the senior team, netting on his Robins debut in a 4-1 defeat to Millwall back in May 2021.
Conway’s moment however was played behind closed doors with no spectators permitted, meaning his friends and family weren’t there to share the moment.
This wouldn’t be taken away from the youngster this time though as his father watched on as one of the hardly 400 souls at the Pirelli Stadium.
He said to the club’s official social media channels: He (Conway’s dad) was up there and it was quite a special moment when I scored.
“I could see him so it was a special moment for him, I’m buzzing to get the goals tonight and get through to the next round.
“When Andi scored it was the icing on the cake. The fans were excellent, they came even though the venue got changed.
“I thought they were excellent and fair play to them. I thought we coped well with the Coventry fans as they made it lively at times. We are through to the next round and that’s the most important thing.”
The 20-year-old recently penned a new three-year contract with the club, outlining the faith City have in one of their younger players.
Conway is a certified first-team player and has come off of the bench in the last two Championship matches after being in-and-out of squads last season.
He is highly thought of by first-team manager Nigel Pearson and will be kept around Ashton Gate this summer rather than any potential loan move to a lower-league outfit.
The two defeats to Hull and Sunderland have been a frustration given the performance had been there to pick up points in the league.
Despite it being in the Carabao Cup rather than the league, there is now that weight off their shoulders that they have claimed their first win of the campaign which they can hopefully use as a springboard against Wigan Athletic.
“We knew coming here tonight that we hadn’t won yet,” he said.
“The most important thing for the team was to win and to get through to the next round.
“It was my priority at first but getting the two goals helped the team, I’m buzzing as well and it couldn’t have gone any better.
“We knew we hadn’t started quick this season, it was to get out there, show the fans we mean business tonight and we scored three goals in the first half. In the second half, it was more of a tight game, with long balls and a bit of a scrappy game.
“We coped well especially when they scored, we kept at it and kept on doing our stuff eventually we got the last with Andi. It was a good performance from the boys
“Whoever comes into the team, we know what our roles are. We work on it day in and day out anyways. It was just a change of personnel, it doesn’t matter who is playing, we know what our jobs are for the team, so it’s going on the pitch and implementing that when the game comes round.”