The 18th-ranked Buckeyes dominated around basket as center Jantel Lavender poured in 28 points and power forward Star Allen added 14. Off the bench, center Andrea Walker added nine points and forward Sarah Schulze had six.
In all, Ohio State scored 48 points in the paint compared to 18 for the Black Knights.
Some of those points for the Buckeyes were via 14 offensive rebounds that led to 22 second-chance points.
Lavender also had 10 rebounds while Walker and Allen both had five and guard Shavelle Little had six.
"We knew coming in this was going to be a huge challenge," Army coach Dave Magarity said after his team fell to 0-2. "We've got some size at 6-2, but (Lavender is) really a very special player. I'm shocked that she only had 28 after having 24 at half. Obviously, she's also a great team kid so she's not worried about that."
Just a sophomore, Lavender has already become one of the best players in the nation, and she showed why she was among 30 players placed on preseason watchlists for national player of the year awards.
Magarity, whose Army team lost at home to Ohio State two seasons ago as three-time Big Ten player of the year Jessica Davenport began her senior season in scarlet and gray, said these Buckeyes look better than that team, which finished 29-3.
"They just seem a lot deeper and a lot more skilled," Magarity said. "As good as Davenport was, I just think Lavender adds a whole different dimension to that post spot, and we just couldn't handle her. We tried to double from the opposite post but she gets her shot off too quick. We tried to double with guards, but she's just too powerful."
Beating double-teams was a point of emphasis in the offseason for Lavender, who was the Big Ten co-player of the year last season as a freshman, and that was an area in which she did not give herself satisfactory marks when the Buckeyes opened the season Friday night with a victory over Butler.
"I was ready for the trap from the beginning," she said of the Army game. "I should have been ready for the trap from the beginning against Butler, but it was the first game so I was excited. Today I wanted to just focus on more reverse pivoting and finding my teammates, reversing the ball and getting the second postup. That opens up the post a lot more than just the initial post play."
Prahalis also had seven assists and three steals with just one turnover. She and Little (five steals) helped spearhead an aggressive defensive effort that forced 25 turnovers that led to 38 points.
Erin Anthony led the Knights with 14 points while Alex McGuire had 12, Nalini Hawkins added 11 and Laura Baranek totaled 10.