The 18-year-old Mensik won 70 per cent of his first serves to notch a 7-6, 6-4 victory over fifth-seeded Alejandro Davidovich Fokina of Spain in 93 minutes. O'Connell, in turn, posted a 6-4, 6-4 triumph over sixth-seeded Jan-Lennard Struff of Germany to set up a second-round match versus Finland's Emil Ruusuvuori, who outlasted Italian Giulio Zeppieri, 7-6, 7-5.
Also on Tuesday, Frenchmen Hugo Grenier and Richard Gasquet each won their respective first-round matches while countryman Alexandre Muller was not as fortunate. Grenier seized a 7-6, 7-5 win over Germany's Maximilian Marterer, and Gasquet secured a 6-4, 6-4 triumph over Kazakhstan's Alexander Shevchenko.
Former world number one Murray of Great Britain snapped a six-match losing streak with a 6-1, 7-6 win over Muller, however. Murray will square off versus Mensik in the second round.
Rio Open
Two of the top three seeds, Spain's Carlos Alcaraz and Nicolas Jarry of Spain, were eliminated in their first-round matches in Rio de Janeiro.
Alcaraz, the top seed, retired due to a right ankle injury with the score 1-1 against Brazilian wild-card entrant Thiago Monteiro.
Jarry, the third seed, fell 6-1, 1-6, 7-5 to Germany's Yannick Hanfmann in one hour and 54 minutes. Hanfmann got an early service break for a 2-0 lead in the third set, but Jarry broke back in the seventh game. With Jarry serving to force a tiebreaker, Hanfmann got a match-clinching service break.
Other first-round winners included Argentines Sebastian Baez, Facundo Diaz Acosta and qualifier Mariano Navone, as well as Chile's Cristian Garin, Serbia's Dusan Lajovic and Brazilian qualifier Felipe Meligeni Alves.
Los Cabos Open
Japan's Yoshihito Nishioka needed just 49 minutes to oust Italian qualifier Flavio Cobolli 6-1, 6-0 in first-round action at Los Cabos, Mexico.
Nishioka never faced a break point and converted six of his seven break opportunities. He won 18 of the 20 points on Cobolli's second serve.
Australia's Rinky Hijikata scored a 6-3, 7-6 victory over sixth-seeded Miomir Kecmanovic of Serbia. Eighth-seeded Jordan Thompson of Australia defeated Mexican wild-card entrant Ernesto Escobedo 6-4, 6-3.
Portugal's Nuno Borges and US players Marcos Giron and Emilio Nava also advanced. Australia's Aleksandar Vukic squeezed past Rodrigo Pacheco Mendez 7-6, 7-6, as the 692nd-ranked Mexican wild-card entrant failed to take advantage of one set point in the opening set and four in the second-set tiebreaker.
