In a match between the WTA's two World No.1s - Williams in singles, Peng in doubles - it was Williams who looked far more comfortable on Manolo Santana court, holding all nine of her service games - and throwing down 11 aces along the way - en route to a comprehensive 6-2, 6-3 victory in 61 minutes.
"I think it was a little tougher than the scoreboard showed," Williams said. "She's a great player. She has had a good last 12 months. She's really coming to age and showing her own. So it was tough.
"But it helped that I had two days off before this. It helped my preparation - it was perfect."
Williams leads Suárez Navarro in their head-to-head, 3-0, losing five games in six sets.
"I'm literally taking it one day, one match at a time and not putting any pressure on myself," Williams said of her chances going forward. "That's how I'm doing it here: literally one match at a time."
If Williams beats Suárez Navarro on Thursday she will become the 11th player in WTA history to reach 650 career match wins, after Martina Navratilova, Chris Evert, Steffi Graf, Virginia Wade, Arantxa Sánchez-Vicario, Lindsay Davenport, Conchita Martínez, Evonne Goolagong Cawley, Billie Jean King and Venus Williams (who is actually just ahead of her little sister with 651 career match wins).
A little later, in a battle of former World No.2s, No.3 seed Agnieszka Radwanska pulled off a miracle win over one of her biggest nemeses, Svetlana Kuznetsova, snapping a six-match losing streak against the Russian with a 6-3, 4-6, 7-6(6) victory. Kuznetsova had all kinds of chances - she led 4-1 in the third set and even brought up triple match point up 6-3 in the breaker - but Radwanska hung tough.
"Of course, 6-3 down in the tie-break, it's never a great situation, especially since she was serving twice," Radwanska said. "But you're still in it until you shake hands. Everything can happen. You can always turn the match around. Fighting to the end is the most important thing in tennis, I think."
Next up for Radwanska is Roberta Vinci, who continued to revive her season with a 6-3, 6-3 win over No.13 seed Caroline Wozniacki. It was straight sets but it all came down to the big points - while Wozniacki converted on just two of 12 break points, Vinci was an absolutely perfect five-for-five.
Radwanska leads Vinci in their head-to-head, 6-1, which includes a 4-0 record on clay.
Other winners during the day were No.4 seed Simona Halep, who beat Spanish wildcard Lara Arruabarrena, 6-4, 6-4, and French qualifier Caroline Garcia, who won by walkover against Maria Kirilenko when the former Top 10 player had to withdraw beforehand because of a left wrist injury.
The night session had its share of drama as well. After No.15 seed Sabine Lisicki beat Romanian wildcard Irina-Camelia Begu, 63 64, Anastasia Pavlyuchenkova did the same to No.6 seed Jelena Jankovic, rallying from 4-1 down in the third to beat her for the fourth time in six tries, 62 57 76(3).