Freshman Justin Jackson added 17 points as the Tar Heels shot 69 percent (18 for 26) after halftime and 60 percent for the game.
The Tar Heels led 40-34 at halftime, but Meeks scored three straight baskets out of the break to push the lead to double digits and put UNC in firm control.
Codi Miller-McIntyre scored 20 points to lead the Demon Deacons (9-10, 1-5), who played tough in losses to highly ranked Duke and Louisville here earlier this month.
But after weeks of clear progress under first-year coach Danny Manning, they took a big step back against the Tar Heels.
Wake Forest shot 40 percent for the game and couldn't keep up with the Tar Heels after halftime, trailing by as many as 18 midway through the second half.
The Tar Heels were coming off Sunday's sluggish home win against Virginia Tech in a performance that irked coach Roy Williams so much that he made his team practice the next night instead of having Monday off.
His team at least responded with a sharper performance despite losing freshman guard Theo Pinson to a foot injury and getting into some foul trouble early in the second half.
Both Johnson and Meeks went 8 for 11 from the floor, while Meeks finished with eight boards despite playing limited first-half minutes after picking up three fouls.
Jackson chipped in his second straight double-figure scoring game, as the Tar Heels scored on 12 of 16 possessions to start the second half. They took a 65-48 lead on Jackson's basket near the 12-minute mark.
UNC: Pinson exited with a left foot injury with 7:52 left in the opening half. UNC was already down freshman point guard Joel Berry II as well as seldom-used reserves Stilman White and Luke Davis. ... UNC has won nine of 10 since losing at top-ranked Kentucky on Dec. 13, with the only loss coming by a point against now-No. 8 Notre Dame.
Wake Forest: The Demon Deacons finished with a 13-7 advantage on the offensive glass, though that led to only a 13-10 edge in second-chance points. ... Devin Thomas had 12 points and 12 rebounds.
UNC hosts Florida State on Saturday.