Szoboszlai netted his first European goal of the 2026/27 season, to haul Andoni Iraola's team level at 1-1 at home to Atletico Madrid, before Mac Allister fired home the winner at Anfield.
Victory on Merseyside marks a winning UCL debut for Iraola as Mac Allister's goal piles more focus on his claims of the club not offering him a contract renewal.
The Atleti clash is the third successive game they have started together at the base of Liverpool's midfield this season, with Mac Allister on the bench for the opener at Newcastle United, as Ryan Gravenberch started.
"I’ve said it many times, I love to play with Macca," Szoboszlai said at full-time.
"We know each other, and he knows what I want to do, and I know exactly what he wants to do - I think that helps the team as well.
"It’s the manager’s decision who will play the next games and I think everyone is ready to compete with each other, but we have to become a family.
"Can we be a successful pairing long-term? We can, we can."