Berdych, whose form has been called into question following a meek third round Australian Open exit, was stretched to the limit by the Romanian but proved too strong in the end.
He will play the winner of Viktor Troicki’s battle with Richard Gasquet.
Closely fought encounter
The match remained on serve throughout the opening twelve games, with Berdych slamming down eleven aces in total to force a tie-break.
He swept the breaker 7-3 and proceeded to break Copil in the second set – his only break of serve all evening – to seal his place in the second round.
“I won in 2014, but I'm not superstitious. It would be a nice tradition to do it, to win again,” the world number 13 said upon his arrival in Rotterdam.
“I like to come here, it's always a tough field with a lot of good players.”
Richard Krajicek, the tournament director, was rocked by news that both Rafael Nadal and Stan Wawrinka had withdrew from the 500-level tournament but he can take solace from a remaining field that promises to make compelling viewing.
Alexander Zverev and Grigor Dimitrov, who claimed silverware in Montpellier and Sofia respectively this past week, headline the pack, with the likes of David Goffin and Jo-Wilfried Tsonga sure to make a fist of it.
Frantic opening day
Elsewhere on day one, Pierre-Hughes Herbert stunned Feliciano Lopez to advance, 7-6(5), 7-6(5).
Local hero Robin Haase knocked off German Florian Mayer, 7-5, 7-6(3), while Denis Istomin, who entered the tournament as a lucky loser, exacted revenge on Britain’s Alijaz Bedene, 6-3, 7-6(3).
Russia’s Evgeny Donskoy, meanwhile, defeated the Spaniard Marcel Granollers, 6-4, 6-4.