Ajla Tomljanovic secured a routine first-round win over Irene Burillo Escorihuela at the Grand Prix Sar La Princesse Lalla Meryem in Morocco, while Magda Linette made comfortable progress at the Internationaux de Strasbourg.
Second seed Tomljanovic wrapped up a 6-2 6-1 win over her Spanish opponent in Rabat on Sunday, kick-starting her bid to better her second-placed finish at the 2018 edition of the event.
The world number 44, who was beaten by fellow Australian Ashleigh Barty in the Wimbledon quarter-finals after overcoming Emma Raducanu in London last year, is on course for a potential meeting with Croatian 16-year-old Petra Marcinko, who shocked ninth seed Rebecca Peterson to claim a three-set victory.
The Australian Open girls' champion and junior world number one claimed a superb 6-0 2-6 7-5 win over the Swede for her first career top 100 triumph.
At the Internationaux de Strasbourg, meanwhile, eighth seed Linette saw off Varvara Gracheva 6-3 6-0 to reach the round-of-16, setting up a potential tie with Heather Watson.
Elsewhere, Harmony Tan downed Australia's Samantha Stosur 6-2 6-1 to set up a potential round-of-16 meeting with Shuai Zhang, who faces Belgium's Maryna Zanevska on Monday.