Rain in recent days has softened Augusta National, making the often rapid and challenging greens much more benign, and the trio seized a two-stroke lead over American Cameron Young and Australian Jason Day.
Favourite, defending champion and world number one Scottie Scheffler was one of seven players sitting three strokes behind the leaders after shooting 68.
But five-time Masters champion Tiger Woods looked more likely to be fighting to avoid the cut than for the title after he shot a two-over par 74 in a round that included five bogeys.
Hovland, who was playing in the same group as Woods, got off to a flying start with an eagle on the par-5 second hole, where he followed up a brilliant iron shot with a 25-foot putt.
Further birdies came on the ninth, 11th and 13th holes but the Norwegian was less tidy in the final five holes, finding himself in trouble on the par-5 15th, where he went far to the left but he was able to scramble to make par as he ensured he finished bogey-free.
"I would have taken that. That was pretty fun. My game's been feeling good," he said.
"But to shoot a 65 bogey-free out here, some things have to go your way. It's not like you can just step up and have that handed to you. So I definitely had some things go my way today but also hit a lot of great shots."
Rahm's score was even more impressive given that he started with a double bogey on the first hole after four-putting.
The world number three quickly made amends with successive birdies and an eagle on the par-5 eighth, where his 249-yard iron shot landed four feet from the pin.
He reached the turn three-under and an excellent back nine left the Spaniard with a share of the lead and in the strongest position of the pre-tournament favourites.
"If you're going to make a double bogey, might as well do it on the first hole of the tournament when you have plenty of holes to make it up," quipped Rahm.
Koepka, who plays in the breakaway LIV Golf League, made eight birdies with a bogey coming on the newly extended par-5 13th hole, where he pulled his drive.
He birdied the final two holes to join Rahm and Hovland atop the leaderboard.
Rough start for Tiger
Woods made three bogeys in his opening seven holes but he recovered slightly with a birdie on the par-5 eighth, where he almost chipped in for an eagle.
After a bogey on the 11th, Woods again bounced back with birdies on the 15th and 16th before his efforts were a little undone by a bogey on the 18th where he found himself in sand trouble.
"I felt like I drove it good," said Woods, "I just didn't do the job I need to do to get the ball close. Today was the opportune time to get the ball - get the round under par, and I didn't do that today.
"Most of the guys are going low today. This was the day to do it. Hopefully tomorrow I'll be a little bit better, a little bit sharper, and kind of inch my way through it."
Scheffler got himself into the groove with an eagle on the second and despite missing some birdie opportunities was well-placed for a second-round push.
"I did a good job of controlling my emotions today and staying in check, and I didn't get too frustrated on the greens. Sometimes they go in, sometimes they don't," he said.
Also on 68 were Ireland's Shane Lowry, Americans Xander Shauffele, Sam Burns and Gary Woodland along with Australian Adam Scott.
The action got underway after former winners Jack Nicklaus, Gary Player and Tom Watson provided the traditional ceremonial launch to the year's first major tournament.
Reigning US Amateur champion Sam Bennett had a memorable round, matching Sheffler's score with his bogey-free round.
World number two Rory McIlroy finished on even par after an inconsistent round that saw him make five birdies, three bogeys and a double bogey on the par-4 seventh.
Tee times for Friday were advanced 30 minutes for a 7.30am start with rain and wind forecast for late Friday through Saturday, which could hurt those caught on the course at the wrong time.
