The pair linked up in the doubles in the first match on Sunday only to go down to defeat to Jack Sock and John Isner.
That gave Team World an 8-7 lead – the first time in Laver Cup history that their side had been ahead in the tournament.
Zverev cut a nervy figure in the doubles and it was up to Federer to restore Team Europe’s advantage with a thrilling win over Isner in the singles.
That left Team Europe just one win away from retaining the trophy with Zverev having the chance to clinch it against Kevin Anderson.
Federer was keen to take the pressure off the German and backed him publicly in an on-court interview before the match.
“The good thing is we could lose the next one and I think Sascha knows that,” he said. “I think that takes the pressure off.
“That’s why the first or second match was so vital for us to get at least one of those two and that puts Novak [Djokovic] in play at the end, who I’m very confident of.
“I’m very confident in Sascha too so it’s just another great couple of matches coming up.
“He’s a terrific player, a great champion already at a very young age.
“He played an unbelievable doubles with me and hopefully it gives him some extra energy right now.”
Team Europe need just one more win from the final two games to take the title.
Team World, meanwhile, need both Anderson and Nick Kyrgios, against Djokovic in the last match on, to come out on top.