Down Mexico way, at the Abierto Zapopan Open in Guadalajara, top seed Nadia Podoroska needed 3 sets and 2 hours and 20 minutes to beat local qualifier Giuliana Olmos in her opener, and surviving a thrilling challenge.
The Argentine, who reached the semi-finals at the 2020 French Open, claimed a 7-6(6) 3-6 6-2 win over the Mexican, and the World No 45 next will play another qualifier in Italian Elisabetta Cocciaretto in the second round.
Wild card Eugenie Bouchard from Canada also reached the round of 16 with a 3-6 6-1 6-3 over American qualifier Caroline Dolehide.
Although Dolehide took the lead in the match by winning the first set, Bouchard, the 2014 Wimbledon finalist, fought back to post an impressive come-back win in an hour and 44 minutes.
The Canadian will take on the No 8 seed Kaja Juvan from Slovenia next for a place in the quarter-finals.
Juvan, who is ranked 91, defeated Aliona Bolsova from Spain in straight sets, 7-5 7-6(7), in an hour and 47 minutes in their opener.
The two seeds who played their respective openers in the bottom half of the draw made their way safely into the second round, with another Spaniard, No 4 seed Sara Sorribes Tormo, defeating Belgium’s Greet Minnen, 6-7(4) 6-4 6-1 in 2 hours and 19 minutes.
In the second round, the 70th ranked Spaniard will play Swiss qualifier, Leonie Kung, who defeated Serbia’s Nina Stojanovic, 6-2 6-3.
Canada’s Leylah Fernandez, the 7th seed, needed 3 sets to get past Russia’s Anna Kalinskaya, 7-5 4-6 6-4.
The 87th ranked Canadian plays Aussie Astra Sharma for a place in the last 8, while Slovenian Tamara Zidansek and Cathy McNally from the US will take on each other in the round 2.
Zidansek posted an upset the 3rd seed Anna Blinkova in the first round, 6-3 7-5, in an hour and 24 minutes, while McNally took the last win of Tuesday by defeating fellow American, wild card Katie Volynets, 6-0 3-6 6-4, in 2 hours and 5 minutes.
In the 9th game of the deciding set, Volynets saved a couple of match points, forcing McNally to serve out the set.
McNally faced 2 break points In the 10th game for a break-back for 5-all but squashed them successfully en route to ending the match on her terms.