Three-time champion Venus Williams saved three match points en route to a 5-7, 6-3, 7-5 third-round victory over Kiki Bertens at the Miami Open on Sunday.

Williams, ranked eighth in the world, will battle for a quarter-final berth against defending champion Johanna Konta, a 6-2, 6-1 winner over Belgian Elise Mertens.

The 37-year-old Williams was cruising with a 5-0 lead in the opening set, but she squandered three set points as Bertens, ranked 29th in the world, rallied to take the set 7-5.

The second set was another streaky affair, but Williams gained a decisive break for a 5-3 lead and fought off a break point in the next game to force the decider.

The seven-time Grand Slam champion would have to dig deep when she fell 1-4 down to her Dutch opponent in the third.

Bertens served for the match at 5-3 but was unable to convert two match points as Williams broke to put the match back on serve.

Williams would face one more match point against her own serve in the next game, but she held on.

She won the last four games of the match as Bertens appeared to struggle with cramps.

Williams sealed the win with an emphatic forehand winner, giving a little leap of elation.

"It didn't look good sometimes, that's why you keep playing until the last point," Williams said. "And that's why I love this game."

Women's results 3rd rd

• Jelena Ostapenko (LAT x6) bt Beatriz Haddad Maia (BRA) 6-2, 7-6 (7/2)
• Ashleigh Barty (AUS x21) bt Petra Martic (CRO) 6-4, 6-3
• Venus Williams (USA x8) bt Kiki Bertens (NED x29) 5-7, 6-3, 7-5
• Johanna Konta (GBR x11) bt Elise Mertens (BEL x22) 6-2, 6-1
• Danielle Collins (USA) bt Donna Vekic (CRO) 4-6, 6-2, 6-1
• Monica Puig (PUR) bt Maria Sakkari (GRE) 6-3, 7-5