Bryant, who is ranked No. 2 overall in the MLB.com prospect rankings, was selected second overall by the Cubs out of the University of San Diego in the 2013 First-Year Player Draft, one pick before the Rockies took right-hander Jon Gray out of Oklahoma.
Arenado's homer to left field came off Cubs starter Jason Hammel, who gave up four hits in two innings.
"It always feels good to hit the ball hard and drive the ball," said Arenado, who also doubled off Felix Doubront. "But there's still a lot of work to be done. I'm not feeling totally comfortable up there, but it was nice to see the ball well today."
Arenado's homer came after Brandon Barnes walked and Roger Bernadina singled, both in lengthy at-bats against Hammel.
"I didn't envision throwing 20 pitches to the first two batters of the year of my 2015," Hammel said. "Hats off to the first two batters for working me deep. A long inning to start the year is always fun.
"Honestly, it was a stupid pitch to Arenado. He didn't take a good hack on my slider before, so I should've gone back to it. It's just [Miguel Montero] and me getting on the same page. First one out of the gate."
Cubs outfield prospect Matt Szczur added a solo shot to left-center in the ninth inning off right-hander Justin Miller.
Bryant's homer was a blemish on an otherwise positive performance by Rockies non-roster right-hander Brett Marshall, who started because lefty Jorge De La Rosa was skipped with tightness in his left groin. Marshall gave up two hits -- a Jorge Soler single, followed by Bryant's homer -- and struck out two in two innings. Marshall's fastball ran 90-94 mph.
Marshall debuted in the Majors with four relief appearances for the Yankees in 2013. Last year, Marshall was told on the day of the next-to-last Spring Training game he had made the Reds' Opening Day roster, but he suffered a strained tendon in his right middle finger that day and was limited to 16 Triple-A starts. This winter he signed a Minor League deal with the Rockies.
"I just wanted to come in healthy and strong, make sure I can battle for a job," Marshall said.
Up next for the Cubs: Jake Arrieta makes his first Cactus League start on Sunday (3:05 p.m. CT, Gameday Audio), when the Cubs play host to the Rangers at Sloan Park. Arrieta is coming off a stellar season with the Cubs in which he went 10-5 with a 2.53 ERA. He was limited last spring because of tightness in his right shoulder but has had no problems this year. Tsuyoshi Wada was scheduled to follow Arrieta. The game will be broadcast on WBBM radio with Pat Hughes and Ron Coomer at the mic.