Britons Jodie Burrage and Harriet Dart came back to win their first-round matches in three sets at Eastbourne, but Heather Watson went out.
Wildcard Burrage, 23, beat Petra Martic 3-6 7-5 6-3 to set up a meeting with Spanish top seed Paula Badosa.
British number two Dart won 3-6 6-1 6-4 against American Madison Brengle and will face Swiss player Jil Teichmann.
However, Watson fell to a 7-6 (7-1) 6-4 defeat by Canada’s Rebecca Marino, who will play Italian Camila Giorgi next.
Eastbourne is the final WTA event in the UK before Wimbledon begins on 27 June.
In the men’s draw, Jack Draper recorded a straight-set victory over American Jenson Brooksby.
Draper, 20, claimed a 6-2 6-2 success and did not face a single break point against the 21-year-old world number 34 as he coolly served out both sets to love. He will now face fourth seed, Argentina’s Diego Schwartzman, in the last 16.
Meanwhile, Jay Clarke lost in straight sets against American 20-year-old Brandon Nakashima, who prevailed 6-1 6-3.
Nakashima will face British number one and top seed Cameron Norrie, who received a first-round bye.
Burrage, ranked 169th, trailed by a set and a break against world number 80 Martic, but rallied superbly from 5-3 down in the second set to seal victory.
The 23-year-old Briton won four successive games to level the match but lost the opening game when serving at the start of the crucial third set.
However, Burrage established a 4-1 lead with two breaks in quick succession, before serving out an impressive comeback victory over Croatia’s Martic.
Dart, 25, had led 3-0 in the opening set against Brengle but the American battled back, claiming six successive games to move one set from success.
The momentum swiftly shifted back in the Londoner’s favour following an exchange of breaks early in the second set, recording a five-game streak of her own to level the contest.
Dart appeared to have made the decisive breakthrough in the final set, taking a 5-3 lead, but she had to hold her nerve after Brengle immediately responded – sealing victory on her 32-year-old opponent’s serve.
British number three Watson, ranked 120th, was handed a lucky loser place in the main draw following defeat by Ukrainian Lesia Tsurenko in qualifying on Sunday.
After conceding the opening set by losing six successive tie-break points, Watson, 30, broke back to level at 3-3 in the second set, but Marino saw out the match after converting her third break point in the following game.
British number one Emma Raducanu is not taking part as she aims to recover from a side injury before Wimbledon.
Dan Evans begins his campaign on Tuesday, against Frenchman Adrian Mannarino, while fellow Briton Ryan Peniston meets French Open quarter-finalist Holger Rune.