Koepka, one of 17 LIV Golf players left in the field after Kevin Na (39) withdrew midway through his round, shot a seven-under-par 65 in ideal scoring conditions at humid Augusta National to join world number three Rahm and Norway's Hovland in the lead.
"There's only really a couple things I care about, is going to work out and going to play golf and that's it when we're here, and nothing else really matters," Koepka told reporters. "It's full focus on this and trying to walk out of here with a Green Jacket."
Cameron Young (25) was two shots off the lead while world number seven Xander Schauffele (29) and former majors champions Shane Lowry (36), Adam Scott (42) and Gary Woodland (38) were all a further shot back.
The only blemish on the scorecard for Koepka, who won last week's LIV Golf event in Orlando, was a bogey at the par-five 13th but the four-time major winner birdied 15 and 17 before draining an eight-foot birdie at the last.
But Koepka, finally looking comfortable after a knee injury that took a toll on his body, responded with birdies at the 15th and 17th before draining an eight-foot birdie putt at the last.
Hovland, who stood out as much for his play as the bold floral pattern on his shirt, fired his lowest score in a major while Rahm caught fire after a four-putt, double-bogey at the first hole.
Hovland made his move early as he rolled in a 25-foot eagle putt at the par-five second and added three birdies across a four-hole span from the sixth to reach the turn at five under.
SHAKY START
Playing in a group with Tiger Woods (47) and Schauffele, Hovland made a sensational par save at the 10th after an errant approach left him with a tough chip without much green to work with and then padded his lead with a 37-foot birdie at the 11th.
Hovland picked up another birdie at the new-look par-five 13th, and then capped his day with a string of pars for his first sub-70 round at Augusta National.
"I don't care how good you hit it out here, you have to chip the ball. You have to have a short game," said Hovland.
"And especially on that back nine when I hit a lot of bad shots, to be honest, but I managed to keep myself in it by hitting some really nice chips and making some really nice putts."
Rahm overcame his shaky with a pair of birdies on the second and third holes and never looked back.
The Spaniard then charged up the leaderboard when he followed a birdie at the seventh with an eagle at the eighth where he stuffed his approach shot to four feet before capping his round with the fourth of his back-nine birdies.
Woods, who has never missed a cut at Augusta National as a professional, teed off having played one event this year and the rust showed as he rarely gave himself any opportunities and admitted to feeling sore after a 74 that was his worst Masters start since 2004.
The five-time champion salvaged his round with two late birdies but closed with a bogey after an unfortunate break off the tee that forced him to take an awkward stance on his approach with his right foot in the sand and the other in the grass.
"I felt like I drove it good. I just didn't do the job I need to do to get the ball close," said Woods. "Today was the opportune time to get the ball - get the round under par, and I didn't do that today."
Tournament favourite Scheffler, bidding to become the fourth player to repeat as Masters champion, mixed an eagle with three birdies and a bogey for an opening 68 that marked the lowest first-round score by a defending champion at the Masters since Tiger Woods in 2020.
"Got a lot of good looks and I thought I was hitting a lot of good putts, just hitting a lot of edges, which happens," said Scheffler. "These greens are not easy to putt and you can't expect to make everything."
Rory McIlroy, who is making his ninth attempt at completing the career Grand Slam, opened with a 72.
Meanwhile, with a one-under 71, 63-year-old Fred Couples became the oldest player to record an under-par score at the Masters since Tom Watson in 2015.
