The world number one looked to be in complete control as Paire struggled late in the first set, but the Frenchman dominated the second before missing chances in the decider, squandering two match points.

Although Federer eventually progressed 6-3 3-6 7-6 (9-7), he knew just how hard he had been made to work for a win that keeps him on course to remain on top of the rankings.

"It was a tough match. I played at a good level actually," the Swiss said. "I think he served well and had a good mix and a good variety. It was hard to break.

"Naturally, it was always going to be tight. And at the end, it was just extremely close. I'm fortunate to have made it."

With Alexander Zverev and Dominic Thiem already out of the competition, Federer's path towards a second consecutive Halle title is clearing - and that continued on Thursday.

Federer will play Matthew Ebden, who knocked out Philipp Kohlschreiber 4-6 6-1 6-2, meaning there are only two seeds remaining in the tournament.

Borna Coric, Zverev's conqueror, won again to set up a clash with Andreas Seppi.