Ruud, the second seed, beat Andreozzi in 2 hours, 49 minutes, 27 seconds.
The American Taylor Fritz, third seeded, defeated his compatriot John Isner in three sets with partials of 3-6, 6-3 and 6-4 in one hour and 53 minutes.
For his part, the American Frances Tiafoe also beat the Japanese Yoshihito Nishioka in two sleeves with a slate of 7-6 (8/6) and 6-4 in one hour and 44 minutes.
The Danish Holger Rune, seeded fourth, defeated the American Ben Shelton in three sets with partials of 6-7 (7/9), 6-4 and 6-2 in two hours and 20 minutes.
The Mexican Open is an ATP 500 category tournament that distributes a bag of 1.8 million dollars in prizes; it is played on the hard surface courts of the GNP Arena and two alternative courts.
Monday’s results in the first round:
Aylor Fritz (USA/N.3) defeated John Isner (USA) 3-6, 6-3, 6-4
Denis Shapovalov (CAN) def. Miomir Kecmanovic (SRB) 6-7 (4/7), 6-0, 7-5
Michael Mmoh (USA) def. Marcos Giron (USA) 7-6 (7/3), 6-1
Frances Tiafoe (USA/N.6) def. Yoshihito Nishioka (JPN) 7-6 (8/6), 6-4
Feliciano Lopez (ESP) def. Christopher Eubanks (USA) 7-6 (7/3), 6-4
Holger Rune (DEN/N.4) def. Ben Shelton (USA) 6-7 (7/9), 6-4, 6-2
Tommy Paul (USA/N.7) to Emilio Gomez (ECU) 6-1, 7-6 (7/4)
Daniel Taro (JPN) def. Jeffrey John Wolf (USA) 6-4, 6-4
Casper Ruud (NOR/N.2) def. Guido Andreozzi (ARG) 6-4, 4-6, 7-6 (7/2)