The midfielder, who joined on loan from Atletico Madrid in January, struck from distance in the 12th minute to give Tottenham an early lead at Aston Villa. Richarlison headed home a second before the half-hour mark and although Emiliano Buendia nodded in a late consolation for the hosts, De Zerbi's side held on comfortably to make it back-to-back Premier League victories for the first time since December.
Speaking to TNT Sports after the final whistle, Gallagher reflected on a result that has transformed the mood around the club.
"We're really happy with the performance and the three points. It's been a perfect night but hopefully it's just the start. We want to carry it on for the last few games of the season."
He spoke about the moment his goal went in.
"It's a good goal. I'm really happy with my first goal. It's always a relief to get the first goal and hopefully a few more can come now."
On the impact Roberto De Zerbi has had in a short time since replacing the sacked Igor Tudor in March, Gallagher was unequivocal.
"I can't speak highly enough of him. He's been so good. Every player in the squad has taken to him — he makes you feel so good. He brings the best out of you."
He extended the tribute to the supporters, who have endured one of the most testing seasons in living memory alongside their team.
"They've had a really rough time this season, along with us. We're all one. Hopefully this can be the start of something great."
Tottenham sit one point above third-bottom West Ham with three games remaining, against Leeds United, Chelsea and Everton. All three are winnable. The first, away to Leeds on Monday evening, is the most demanding — Daniel Farke's side are in form and fighting for their own survival at the other end of a season that has gone far better than most expected.
West Ham's 3-0 defeat at Brentford on Saturday left the door open for Spurs, and they stepped decisively through it.