The game matched traditional NCAA Football Championship Subdivision powerhouses. Eastern Washington is ranked first and Sam Houston 14th in the FCS coaches' poll.
Adams completed 26 of 48 passes with one interception. Quincy Forte added 152 yards on 23 carries for the Eagles, who had 624 total yards.
"That quarterback is really special," Sam Houston coach K.C. Keeler said. "He's a young man who made a lot of big plays."
Overthrows and dropped balls kept Adams from making several big plays. The game was tied 21-21 at halftime.
"I was getting IVs (in the first half)," Adams said. "I was cramping up, and my quarterbacks coach (Zak Hill) told me I had to work on my technique. In the first half, I was nervous and sloppy."
For Sam Houston, Jared Johnson passed for 317 yards, two touchdowns and two interceptions. Keshawn Hill ran the ball 17 times for 133 yards and one touchdown. The Bearkats had 542 total yards, but were hurt by 16 penalties for 159 yards.
"Just way too many (penalties)," Keeler said. "They're a good football team. We had to play cleaner to have a chance to win."
Eastern Washington coach Beau Baldwin said some of the Eagles displayed "antsy nerves" in the season opener.
"We were off on little things," Baldwin said, "but once we settled down, it was fun."
Adams and Johnson scrambled impressively on a number of occasions. Adams, a second-team All-American last season, finished with 61 yards on 12 carries. Johnson had 79 yards on 10 carries, including a 53-yard touchdown run in which he had a strained hamstring.
Eastern went ahead to stay when senior Lynden High School product Blair Bomber caught his second touchdown pass midway through the third quarter.
Keeler, coaching the Bearkats for the first time after a successful run at Delaware, said "two of the better receiving corps in the country" contributed to the high points and yardage totals.
Still, Keeler was disappointed in his team's defensive play.
"Just too many big plays," he said. "Too many mental mistakes."
"If you take away a couple big plays, I thought our defense played really well," Baldwin said.
The game, played on the red artificial turf at Eastern's Roos Field, drew a sellout crowd of 10,310. The Eagles had been 0-3 against Sam Houston.