Junior forward Ethan Happ scored 14 points for the ninth-seeded Badgers (15-17), who will face top-seeded Michigan State (28-3) in Friday's quarterfinals.
Freshman guard Brad Davison added 13 points, junior guard Khalil Iverson scored 11 and Pritzl had 10.
Sophomore guard Kevin Huerter scored 20 points for eighth-seeded Maryland (19-13). Sophomore guard Anthony Cowan added 16 points and freshman forward Bruno Fernando had 12 points and nine rebounds.
Pritzl's 20-footer gave the Badgers a 55-53 lead. Maryland later had a chance to tie the game when it trailed by three in the final seconds but Iverson stole the in-bounds pass and hit two free throws with 0.8 seconds left to seal it.
Wisconsin won despite shooting just 36 percent from the field. The Terrapins shot 44 percent while posting a season low for points.
The Badgers led 35-28 after two free throws by Pritzl with 17:31 remaining but Maryland recovered and pulled within 44-43 on a layup by freshman guard Darryl Morsell with 8:57 to go. The Terrapins caught Wisconsin at 47 on Fernando's inside hoop with 4:18 left.
Wisconsin inched ahead by two points three times over the ensuing three minutes and Huerter scored the tying hoop on each occasion, the final time with 1:22 to play.
After Pritzl made the big jumper to give the Badgers a two-point edge, Huerter was fouled with 9.2 seconds to go but missed the first free throw before making the second.
Davison hit two free throws with 8.5 seconds remaining for Wisconsin.
The Badgers held a 28-26 halftime lead despite shooting just 37 percent from the field.
Wisconsin took a 19-12 advantage on Happ's dunk with 9:35 left in the half before missing 10 of 11 field-goal attempts the remainder of the stanza.
The Terrapins recovered to take a 24-23 edge with 1:14 remaining on the strength of six straight points from Cowan -- a 3-pointer and a three-point play.
Pritzl drained a 3-pointer with 12 seconds left to end a field-goal drought of 9:23 to give the Badgers a four-point advantage before Cowan made two free throws with four seconds remaining.
--Field Level Media
Wisconsin | Maryland | |
Ethan Happ 14 | Scoring | Kevin Huerter 20 |
Brad Davison 2 | Assists | Anthony Cowan 4 |
Ethan Happ 7 | Rebounds | Bruno Fernando 9 |
Ethan Happ 6 | Free Throws Made | Anthony Cowan 3 |
Brevin Pritzl 3 | Steals | N/A |
Ethan Happ 2 | Blocks | Anthony Cowan 1 |