It was Clemson's first NCAA Tournament win since beating Tulsa in the second round of the 1997 NCAA Tournament.
And it was convincing.
UAB took an early 5-4 lead, but Clemson responded with a 21-2 run over the next eight minutes and never trailed again.
"We finally got that first round win," Jerai Grant said afterwards. "Everybody worked towards this goal and now we can't take anything for granted. We have to get ready for West Virginia."
The Tigers held Conference USA's Player of the Year and the nation's leading assist maker, Aaron Johnson in check too. While the final box score reveals he scored six points and dished out 6 dimes, he also turned it over five times, before leaving the game at the 5:44 mark with a broken leg.
Grant led the Tigers with a career-high 22 points and eight rebounds. Milton Jennings added 11 points while Devin Booker and Tanner Smith added 10.
Clemson now advances to the second round of this year's field of 68, facing West Virginia Thursday at 12:15 p.m. in Tampa, Fla.
The Mountaineers are seeded fifth in the East Region, while Clemson is No. 12.
"We did a lot of good things in the game," Clemson head coach Brad Brownell said. "I thought our attention to detail was good early. We gave up too many threes but by doing that we swallowed up Aaron Johnson a good bit and that's what we wanted to do.
"We got a lot of deflections and loose balls and forced them into situations to not allow them to get into any really good runs."
The Tigers led 39-27 at halftime on the strength of Grant and Jennings, who combined for 20 first-half points - all of which came in the paint.
Clemson outscored UAB 28-4 in the paint in the first half on the way to establishing a 12-point halftime lead. (AP)
Their hot-shooting continued in the second half but with Clemson leading 50-40 with 10:07 remaining, Tanner Smith hit a fall away jumper from the left side before Devin Booker hit two free throws and Grant made a layup to make it 56-40 with 7:41 remaining.
After a layup by UAB's Cameron Moore cut it back to 14, Andre Young hit his second three to push the lead to 17 and there was no looking back.
The relentless inside game of Grant and Booker kept UAB at bay. The Blazers cut a one-time 20 point lead to 13 with just over 1:30 to play, but by then it was too late.
Jennings responded with a three pointer from the left side to seal to the deal.
"They were a lot bigger and stronger than our guys could adjust to," UAB head coach Mike Davis said afterwards. "They are a well coached basketball team. They played North Carolina hard before North Carolina came back and won. We turned the ball over four or five times in our first 10 possessions and that helped them get that big run."
Demontez Stitt was surprisingly quiet after scoring a career high 25 points in Clemson's overtime loss to North Carolina in the ACC Tournament in Clemson's last game, but he didn't have to shoulder the load against the Blazers as the Tigers outscored UAB 40-12 in the paint.
Stitt finished with seven points and three assists on 3 of 7 shooting.
The Tigers shot 52 percent for the game overall, but made just 4 of 13 three pointers. Conversely, UAB shot 37.5 percent but made 12 of 24 (50 percent) from the behind the arc.
Clemson won't have long to celebrate Tuesday night's win as it immediately boarded a charter flight to Tampa for its second round game against West Virginia.
"The plane ride is going to be draining," Stitt said. "But we have to do the best job possible to get as much rest as we can between now and Thursday."
The Tigers last faced the Mountaineers in the 2007 NIT Championship game, falling 78-73.
But ending 14 years of NCAA misery by beating UAB was the story Tuesday night.
And Brad Brownell and company hope it's a story that's nowhere close to being finished written.