But reigning champion Hansle Parchment of Jamaica could only advance as one of the fastest qualifiers after finishing fifth in his heat, outside the automatic top three spots.
Holloway clocked the fastest time of the day, 13.01 seconds, to win his heat, with the semi-finals scheduled for Wednesday at 1705 GMT and the final a day later at 1945 GMT.
"I'm looking forward to continue each round and obviously it's the Olympic Games so you've got to be on your Ps and Qs each round," Holloway said.
The 26-year-old is a three-time world champion and the second-fastest man in history at the event, with a personal best of 12.81sec.
But he was surprisingly beaten into silver at the Covid-delayed Tokyo Games in 2021 by Parchment.
"The biggest thing is to execute this time and not really worry about the past and continue to show great form. All roads lead to the final," Holloway said.
"I could have done a little better the first half of the race, but that's what rounds are for. As long as I'm able to get better each round, that's the main thing."
Holloway also stressed that the world record of 12.80sec set by fellow American Aries Merritt in Brussels in 2012 was not exactly on his radar in Paris.
"The final, let's just go for the gold. Everybody is talking about a world record. If it comes, it comes, but the first thing we have to take care of is winning," he said.
Parchment clocked 13.43sec in finishing fifth in his heat, but was unruffled.
"Everyone asks about pressure being the reigning champion," he said. "It's never about pressure, it's not part of it, I'm not thinking about it.
"I'm into the semi-finals. I'll take it from there."
'Another opportunity to do my best'
Holloway's US teammate Freddie Crittenden was last of the hurdlers, clocking a comparatively pedestrian 18.27sec in his heat -- almost five seconds slower than heat winner Louis Francois Mendy of Senegal.
But Crittenden admitted his go-slow pace had essentially been a tactical decision to allow him more time to recover from injury.
"I didn't run hard because I had some aggravation yesterday in my adductor (muscle). There's some activation that didn't work and that's caused pain and discomfort," he said.
Crittenden's Olympics are not over, however, as he now goes into the repechage --- introduced to allow a further round of qualification for athletes in their given event.
"The plan was to use the repechage to get through the rounds, not get disqualified. Then I can run hard in the repechage round in two days, when hopefully the discomfort's gone," he said.
"I'm definitely glad the repechage was here today. I'm still trying to learn the rules but now I have another opportunity to do my best."
Crittenden admitted that athletes' use of the repechage could be "strategic".
"If I'd had to really go for it today to qualify I could easily have crashed out. I could have really hurt myself much worse. It would have been all or nothing," he said.
"The Olympics are the biggest event we have, the pinnacle. And for athletes to train really hard to get here and then have just one round to go for, it is really hard.
"This gives them another opportunity to represent their country and themselves, to show all the hard work they've done."
