Golden Eagles coach Buzz Williams called a timeout, and after the short break, Whittington clanked the front of the rim on the third attempt, allowing Marquette to hang on for a 49-48 victory that snapped the Hoyas' seven-game winning streak.
With Marquette leading 49-46, Whittington took a pass from Otto Porter on the baseline and was fouled by Trent Lockett on a 3-point attempt.
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"I was in extreme help mode," said Lockett, who acknowledged he was out of position defensively. "I tried to jump at him and he jumped forward when he shot, and it was all bad from there."
Whittington only had made 62 percent of his free throws this season, but he confidently swished the first two before Williams decided to ice the Georgetown forward.
"The way he stepped up and hit those first two I was, I guess, not so confident he would miss the third one, but I sure was glad he did," Lockett said.
Lockett grabbed the rebound in the lane and was fouled, but missed two free throws and the game ended without the Hoyas attempting a final shot.
"We had our opportunities today and we just didn't convert on a few things," Georgetown coach John Thompson III said. "That's the Big East. Every game, every possession is important."
Lockett, a senior forward who transferred from Arizona State, said there was little difference between the teams during the game.
"We both worked so hard and it's just one little thing, and it's the difference between us having a great, great night and going into tomorrow, and them having a bad plane ride home tonight," Lockett said.
Marquette (11-3, 2-0 Big East) lost at Wisconsin-Green Bay on Dec. 19 but since has won four consecutive games, including its conference opener on Tuesday against Connecticut.
"We can lose to a team that's not really good and we can beat one of the best teams in the nation," point guard Junior Cadougan said. "It's our choice. It's how we come to work every day. Everything depends on our energy."
The Golden Eagles held Georgetown 18 points below their season average of 66 points a game.
"Their offense is so unique," Williams said. "You have to have a very delicate balance in how to prepare for them in how to stop their offense. But you can't become so consumed in what they do that you're not diligent in preparing how to score against them."
Georgetown (10-2, 0-1) lost in its first road game of the season after playing eight home games and three on neutral courts.
Williams said his team won the game due to a 35-26 rebounding advantage.
"It was on the glass," he said. "We had a really strong presence on both ends."
Markel Starks had 14 of his 18 points in the second half while Whittington and Porter added 13 each for the Hoyas.
It was the Hoyas' first game since Dec. 22 and first loss since dropping an 82-72 decision against then-No. 1 Indiana in overtime on Nov. 20.
Gardner was fouled and made one of two free throws to give Marquette the lead for good, 47-46, with 2:01 left.
Georgetown then got two shots off on its next possession, but couldn't score.
Vander Blue drove the lane for Marquette, but was called for an offensive foul with 24.6 seconds left.
The Golden Eagles opened their biggest lead of the second half, 32-27, on two free throws by Gardner with 13:42 left.
The Hoyas went on a 9-4 run and tied it at 36 on Porter's 3-pointer with 10:16 to go.
Blue scored 10 points in the first half and Marquette led 20-19 at halftime despite making only 7 of 27 shots.
Each team played stifling defense in the opening minutes of the game and neither team could score consistently. Marquette missed 11 of its first 13 shots and Georgetown missed 10 of its first 12.
The game was between two schools that announced last month they would be leaving the Big East to form a new conference.