Connecticut (25-6) won its 10th straight game and advanced to meet North Carolina State in the second round.
Okafor, a 6-9 freshman center, repeatedly forced Hampton (26-7) into taking perimeter jumpers with his inside presence. He led the Big East in blocks.
"Before the game, the coaches pointed out that they were small," Okafor said. "I know I had to take advantage of this and show up today. I had to play hard and do what I needed to do."
The Huskies led by as many as 15 points in the first half, but the gritty Pirates, who upset Iowa State last season in the first round, did not quit. Tommy Adams had a layup and a dunk to bring Hampton within 71-67 with 3:05 remaining.
Thanks largely to Okafor's presence, the Pirates did not score again. Connecticut fared only slightly better, but got a pair of free throws by Taliek Brown and a follow shot by Johnnie Selvie for an eight-point cushion with 1:34 remaining.
"I think in the last four minutes he looked up and saw the score and joined in with everybody else to play defense and stop penetration," Huskies coach Jim Calhoun said. "We then had the answer in the middle with Emeka."
"He's the difference maker," Hampton coach Steve Merfeld. "We're just not used to that presence inside. I think he had five blocks and I don't know how many shots he altered."
Caron Butler scored 21 points to lead Connecticut, which turned the ball over 15 times. Selvie had 13 points and 11 rebounds for the Huskies, who held a 43-34 edge on the glass.
Connecticut as if it would run away with the game after two foul shots by Mike Hayes extended the lead to 40-25 with just over four minutes left in the first half. Hampton's Mackell Purvis made a three-pointer that cut the deficit to 46-35 at the break.
A three-pointer by Adams brought Hampton within 53-49 with just under 15 minutes remaining before Connecticut scored seven straight points for an 11-point bulge. But the Huskies were never able to pull away.
"They're a really good basketball team," Butler said. "We just overwhelmed them in the end. Hopefully, we won't face a team like that in the future."
Adams led Hampton with 23 points in his final game and Purvis added 13. Isaac Jefferson finished with 10 points and 10 rebounds.
"You never want to go out with a loss, but the four years I have been here, this program has made great strides," Adams said. "They are slowly growing. These are a great group of guys to be around. I'll miss everything that was out there in college."
The Pirates closed the season by winning 18 out of 20 games. Their last previous loss had also come in Washington, at Mid-Eastern Athletic Conference rival Howard on Feb. 26.