That 62-minute win set up a meeting with Suarez Navarro following the Spaniard's 7-5 7-5 triumph over Kristina Mladenovic - who knocked out Osaka on Tuesday.
Meanwhile, Hsieh Su-wei won the last six games to beat fourth seed Karolina Pliskova 6-4, 1-6, 7-5 and will next face a woman she has never beaten - two-time Wimbledon champion Petra Kvitova.
World number 2 and Dubai Duty Free Ambassador, Simona Halep treated herself this week ahead of her first game at the Dubai Duty Free Tennis Championships with a quick shopping spree at the Dubai Duty Free shop in Terminal 3, Concourse B. "I feel more relaxed in the final set, so I gained the match pretty well".
It was the second major surprise in a week involving US Open champion Osaka, who announced she had parted ways with Sascha Bajin, the coach who had guided her in both her Grand Slam victories.
Bencic profited from a break for a 5-2 lead in the final set but needed three chances a game later to close out victory as Halep drove a forehand long. Previous year in Miami, Pliskova prevailed in the deciding tie break and she was in a flawless position today, opening a significant lead before losing the energy and the drive to lose the last six games of the match and push Su-Wei into the semis.
"I just need to try to play my game and be happy on the court, be positive".
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"See, it's a little bit hard because I feel like people are staring at me, and not in a good way".
"When I came here, I didn't really have many days of practice, to be honest", the two-time Wimbledon victor said. "I was still there", said Swiss star Bencic whose career has been blighted by a series of back and wrist injuries.
"But even if I don't win any matches for the rest of the year, I wouldn't say I'm concerned. It's great when you're not playing your best and you still find a way to win". I wasn't really that prepared for this tournament.
Halep, Dubai champion in 2015, saw off 2014 Wimbledon finalist Eugenie Bouchard 7-6 (7/4), 6-4.
A week after knocking Lesia Tsurenko out in Doha, Simona Halep ended the Ukrainian's participation in Dubai.
"For me, I just want to have the mentality of not thinking so much who is in the other side of the net", the 24-year-old said.