The world No 10 cited the tie-breaker as the turning point in a 7-6 (7/3), 6-1 defeat of Serb Victor Troicki to reach the second round.
"Winning the breaker was the key to the match," said last week's champion in Montpellier less than 60km from his family home in the south of France. "I played well and was then more confident at the start of the second set.
"It was the perfect start for me."
Gasquet has become the first man this season on the ATP to win multiple titles after starting out in January with Doha honours. The last time he won more than one title in a season was 2006 when he claimed three,
"I've only lost once this year," said the 15-1 Gasquet. "Of course I hope to keep going like this. My only defeat was to (Jo-Wilfried) Tsonga in Australia. I'm fighting as much as I can for ranking points, that's why I'm here."
Fifth seed Gilles Simon won his second-round encounter with Italian Matteo Viola 6-3, 6-1 while compatriot Julien Benneteau joined him in the quarter-finals at the Ahoy stadium with a victory over Romanian Victor Hanescu 6-1, 6-3.
German qualifier Matthias Bachinger earned an upset win over Andreas Seppi, the Italian sixth seed, 6-3, 6-4.
Defending champion Roger Federer will open his week with a first-round match against Slovenian Grega Zemlja later.
Latest results on Wednesday during the third day of the ATP Rotterdam Open:
First round
Matthias Bachinger (GER) bt Andreas Seppi (ITA x6) 6-3, 6-4
Richard Gasquet (FRA x4) bt Viktor Troicki (SRB) 7-6 (7/3), 6-1
Second round
Gilles Simon (FRA x5) bt Matteo Viola (ITA) 6-3, 6-1
Julien Benneteau (FRA) bt Victor Hanescu (ROM) 6-1, 6-3