Not until the fifth point did Halep get on the board, but it would be too little, and Bencic served out the set, 7-6 (2), having fired off 22 winners, and she was still ideal at the front of the court.
If Halep wins the tournament she will replace Osaka at the top of the WTA rankings heading into the French Open.
The seventh-seeded Bertens didn't drop a set all week, a first at the Mutua Madrid Open.
Halep, who had won Madrid twice, suffered her second loss in this final.
Osaka will achieve both of those goals if she makes it through to the quarter-finals this week, while Simona Halep must win the title to have any chance of replacing her. Halep reached the final by beating opponents like Johanna Konta, Ashleigh Barty and Belinda Bencic along the way, losing only a set in the semifinal against the Swiss.
Federer saved another match point to set up a tiebreak and he proved unstoppable as he swept to his 1,200th match win. She fell 3-1 in the second set before battling back to force a tiebreaker, which she lost 7-6. "She deserved to win the match definitely". She will face Halep, who she has also beaten this year, in Dubai, in the semifinals. "I think at the beginning, I was a little bit searching for my game still, but I think the rest of the match I played really solid, really smart, and I was just going for my shots", said Bertens.
Venus, unseeded in the Eternal City, came through an almighty tussle with Elise Mertens 7-5 3-6 7-6 (7-4). Stephens had no trouble getting past Petra Martic in her last-eight encounter. The 27-year-old has failed to go past the fourth round in any of the three Grand Slams since. Bertens has a WTA-best 219 aces in 2019. She's the only player to do this in tournament history.
They've split two clay matches.
Petersburg against Donna Vekic (in career she won 8 titles in 10 finals played).
Halep's rally fell short, however, as Bertens stayed calm and continued to punish her on serve.
At three games down, she cried during the changeover, with Halep immediately breaking for 4-0 when play resumed, going on to wrap up the set and the match easily.