The Musketeers (15-4, 5-1 Big East) led by 18 at the half behind scorching starts by Christon and Martin and hung on in the second half after DePaul pulled within seven.
Christon, who came in averaging a team-high 16.3 points, finished one shy of his career high set against Marquette on Jan. 9. He had 19 points in the first half alone and hit nine of 19 shots in the game, with no trouble driving to the rim.
Martin scored 14 in the first half and finished with three 3-pointers to go with seven rebounds, and Xavier hung on after things got tight down the stretch. DePaul was within 72-65 after Billy Garrett Jr. hit a free throw with 5:50 remaining, but the Musketeers' Isaiah Philmore scored on a layup to start a 9-1 run.
Cleveland Melvin led DePaul with 25 points. Garrett scored 18, but the Blue Demons (10-10, 2-5) hit just 22 of 38 free throws on the way to their second straight loss. Wins over Butler and St. John's gave them back-to-back Big East victories for the first time in six years, but after getting blown out by Villanova on Saturday, DePaul came up short again.
Losing two starters to injuries probably didn't help.
Center Tommy Hamilton IV left with a chest injury in the first half while defending a traveling Matt Stainbrook. And guard Charles McKinney twisted his left ankle on defense about six minutes into the second.
Early on, it looked like this would be a blowout.
After rallying from 17 down to beat Georgetown on Wednesday, Xavier led 50-32 after a dominant first half. The Musketeers had no trouble getting inside and they went on a 17-5 run with the game tied at 22 with about eight-and-a-half minutes left in the first half.
Martin started it by banking in a pull-up jumper while getting fouled by Young and hitting the free throw to complete the three-point play. James Farr, from nearby Evanston, Ill., then nailed a 3-pointer, and Christon broke for a dunk after Garrett lost his dribble, making it 30-22.
The Musketeers continued to pour it on after a layup by Young.
Stainbrook answered with a basket and Martin buried a 3 to make it 35-24. Xavier then responded to a 3 by Melvin with a layup by Christon and a neat reverse baseline drive by Dee Davis, who pumped in mid-air, to make it 39-27 and cap the run with just under four minutes left in the half.
The pace slowed in the second half, and DePaul made several pushes but couldn't sustain them.
Terrance Ferguson, a lottery possibility for the 2017 NBA draft, has withdrawn his commitment to Arizona and will play overseas next season.
College basketball coaches across the country will hit the recruiting trail hard in July to target the Class of 2017's top prospects. Which players are the nation's top programs targeting?
With only a handful of players expected to return after next season, John Calipari has Kentucky in the mix for nearly every elite 2017 prospect.