The Seagulls suffered the major disappointment of losing the first Euopa League match in their history against AEK Athens in midweek.
But three days later they came from behind to beat Bournemouth 3-1 to climb to third in the Premier League.
Brighton trailed to Dominic Solanke’s opportunist strike but went in level at half-time after Milos Kerkez headed Gilmour’s cross into his own net.
Boss Roberto De Zerbi, who had made nine changes to his starting line-up from Thursday, sent on Ansu Fati and Kaoru Mitoma at half-time.
And the pair had an instant impact, combining for an exquisite goal just 15 seconds into the second half, with Mitoma applying the finishing touch.
Japan winger Mitoma then wrapped up the victory with a late header.
“We knew we had to bounce back, but the first half wasn’t what we expected, we never really got going, but it was a game of two halves,” midfielder Gilmour told the club website.
“It’s a bit of everything. The disappointment of midweek. The start wasn’t what we’d like, but the substitutes coming on, Ansi and Kaoru, straight away had an impact.
“This was our first game after Europe and we’re getting used to it. I’m enjoying playing my football and to have the trust to play back-to-back games.”