The Belgian needed treatment for a shoulder problem after losing the opening set.
However, Federer came back to take the second set, also in a tie-break, and then won the third set easily to seal a 6-7 (2), 7-6 (6), 6-2 win against Wawrinka.
They have met three times, always in the final, and Federer has won all three in straight sets, 6-1 7-5 in 2009, 6-0 7-6 in 2012 and 7-6 6-3 in 2015. "But it was only after he was treated that I knew something might be wrong". This match was erratic at the start with hardly any rallies. "I've put myself in a good position in the semifinals".
"I'm happy to see where I am right now".
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World number one Halep took advantage of a morning respite from the rain to finish off a 4-6, 6-3, 6-3 victory over Ajla Tomljanovic.
The result sets up the prospect of a mouth-watering final between Djokovic and Roger Federer, one of the greatest rivalries in the history of the sport. I think it's very hard to win Masters 1000s.
"To go back on the court again against Raonic, who was serving 140-plus miles from the first game, that got me going for sure from the beginning", said Djokovic.
"Yeah. Well, I must be very pleased with fighting spirit and staying mentally tough to overcome deficits in both matches", Djokovic said of his efforts after winning the quarterfinal match.
Mayer had a chance to force a third set, but Federer held on to win his third consecutive meeting with the Argentine as players double up in matches in the rain-delayed tournament.
The Serbian first had to finish his Round of 16 match against Dimitrov that was called late last night due to weather.
The Croatian won his only Masters title in Cincinnati and having missed the event previous year his run this week meant he was riding a nine-game winning streak.
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"I feel like I'm trying to defend my title from way back when", he said.
World number 17 Bertens, who played and won two matches on Friday after rain interruptions this week, looked fitter that two-time Wimbledon victor Kvitova in hot, humid conditions.
"I really need to play more aggressive".
"It was a roller-coaster match", added the Wimbledon champion, who admitted he was distracted my loud music coming from outside the court early in the third set.
His determination showed in the first set.
Halep broke in the final game to move through as Sabalenka volleyed long on a second match point after 76 minutes.
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