David Moyes's side fell behind early in the second half when Yann Gboho found the net, but Barry took control of the contest with a decisive double to turn the game around.
The 24-year-old has now scored 10 goals this season, already surpassing his entire tally from the 2025-26 campaign. He has also found the net six times in his last seven appearances across all competitions.
Moyes was particularly pleased with Barry's response after the striker struggled in front of goal during his first season at Everton following his move from Villarreal.
"We gave away a really poor goal but the reaction from there was really good. Important that Thierno Barry got another couple of goals tonight which was huge for us," the Everton manager said.
"He can smile at me now and say I told you so and that's good. We always liked him and we want him to keep scoring."
Moyes added that Barry's finishing had improved significantly, making him an increasingly important player for Everton. "He's missed quite a few chances but tonight he got important goals for us. He's becoming an important piece for us and he's got 10 goals for us which is really good."
Barry revealed that Manchester City striker Erling Haaland is one of his biggest inspirations and admitted he would love to challenge him for the Premier League Golden Boot.
"I'm very happy because I'm a fan of him. I watch a lot of videos of him and try and do the things he does," Barry said. "If I can stay with him until the end to get the Golden Boot I will try."
The victory lifted Everton into fifth place and extended their winning run to three matches in all competitions. Moyes acknowledged that Coventry had made life difficult for his team but was delighted with the response after falling behind.
Coventry manager Frank Lampard, meanwhile, was frustrated by several major decisions, including two penalty appeals involving James Tarkowski and Vitaliy Mykolenko. He also questioned whether Everton's second goal should have stood because of a possible handball. "Big decisions affected the game, clearly," Lampard said.
Lampard, who previously managed Everton, felt VAR had failed to reach the correct conclusions. "The last touch to score is off the hand, in my opinion. I've seen a conclusive angle so I can disagree," he added. However, the decisions stood, leaving Everton to celebrate another important victory and Barry's growing influence.