Jackson had 18 points and A.J. Walton had 11 for Baylor.
Drew Crawford had 19 points for Northwestern, which had five players in double-figure scoring. Sobolewski had 13 points, Jared Swopshire had 12 and Alex Olah scored 10.
Northwestern had a 54-36 lead with 11 minutes left on a 3-pointer by Sobolewski.
The Wildcats were up 66-55 with 3:10 left when Olah, who went into the game shooting only 27 percent from the free throw line, made two free throws. But a minute later, right after Hearn fouled out, Olah missed two attempts to start Northwestern's stretch of six consecutive misses.
Swopshire's reverse layup with 1:03 left made it 70-63, and his key free throw with 9 seconds put the Wildcats up 72-67.
"They just outworked us. They wanted it more than we did," Jackson said. "That's about it."
Isaiah Austin, Baylor's 7-foot freshman, made a 3-pointer with 2 seconds left when he quickly regained control after Sobolweski deflected the ball on his first chance.
The Wildcats will play only three of their first 15 games away from home, all in Texas. They won both games played in the South Padre Island Invitational on Thanksgiving weekend, including a 55-31 win over Big 12 newcomer TCU.
This was only the second meeting between Baylor and Northwestern, and came exactly a year after the Bears won 69-41 at Evanston.
"They beat us good. It was one of the worst games we've ever had. But it's a different team for them, too," Carmody said. "You think that they're big now, but they're not really big. Last year they were big, and they swatted stuff, and they were really good. And this team is good, and they'll get better and better. But we didn't have a chance last year."