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The 35-year-old Murray dropped the first three games of the match but recovered to break O’Connell four times and celebrate his tournament debut with a 95-minute win.
Murray missed much of the clay-court season to focus on his preparations for grass. He reached the semifinals of the Surbiton Trophy last week, when he was beaten by Denis Kudla.
Seventh-seeded Alexander Bublik defeated Kudla 7-6 (3), 7-5 later Tuesday to prevent a rematch. Murray will now face Bublik in the second round.
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Marton Fucsovics came back to beat Austrian qualifier Jurij Rodionov 6-7 (5), 6-3, 6-4 for a second-round meeting with third-seeded Hubert Hurkacz.
Arthur Rinderknech defeated compatriot Ugo Humbert 4-6, 7-6 (4), 6-4, and will next face another French player, Benjamin Bonzi. Bonzi defeated Spain’s Feliciano Lopez 6-4, 6-1 on Monday.
Also, Nick Kyrgios defeated Jiri Lehecka 7-6 (3), 6-3.
The fifth-seeded Nikoloz Basilashvili was leading Lorenzo Musetti 7-5, 4-2 when their first-round match was suspended due to rain.