Elon guard Austin Hamilton gets past Georgetown center Joshua Smith during the first half. (Alex Brandon/AP)

Georgetown boasted the NCAA championship credentials, superior size, greater athleticism and the home-court advantage to boot. But squared off against a mid-major opponent stocked with unselfish sharp-shooters who attacked the boards with an underdog’s fury, the Hoyas found themselves in a battle Tuesday at Verizon Center.

But after a sloppy first half in which they shot poorly and defended even worse, trailing by six at one point, Georgetown rallied for a 85-76 victory over Elon. With it, the Hoyas concluded a four-game homestand against mid-majors with an unblemished mark to extend their winning streak to six games.

Senior point guard Markel Starks paced the team with 21 points, while his backcourt mate D’Vauntes Smith-Rivera added 19. Playing a season-high 30 minutes, 6-foot-10 center Joshua Smith proved his 350-pound weight in gold down the stretch, finishing with 18 points and grinding down Elon’s defenders along the way.

The Hoyas had never trailed in their three previous games, routing Lipscomb, High Point and Colgate by an average of 20 points. Tuesday’s victory was less convincing, with Georgetown (7-2) allowing Elon (5-6) to shoot 58 percent in the first half, getting out-rebounded 31-30 and surrendering 13 three-pointers.

“There’s a lot we can take away from that,” Coach John Thompson III said. “I’m glad at the end of the day we had more points than them.”

Chief among the takeaways: Georgetown needs to do a better job on the boards. On more than one play, the Hoyas defended well for 20 or 30 seconds only to allow Elon an open shot and an offensive rebound.

Elon Coach Matt Matheny conceded that Smith was the one problem his Phoenix couldn’t solve.

“When we play Georgetown, our margin for error it ever so slight,” Matheny said afterward. “Some missed free throws, untimely turnovers are not good for us. And then we had trouble stopping [Joshua] Smith. He was a force inside. We tried multiple defenses, and we were unable to consistently stop him, as well as Georgetown.”

The Hoyas’ competition gets markedly tougher Saturday, when they visit Allen Fieldhouse for the first time in the program’s history to take on perennial power Kansas (7-3), whose ranking has slid to No. 18 after a rockier than usual start to the season.

Before a crowd of 7,586 at Verizon Center on Tuesday, Georgetown took a 10-5 lead, with Elon missing its first three shots. The Phoenix settled down soon after, showing patience and moving the ball crisply. Elon starting hitting from the outside, and its 6-10 forward Lucas Troutman muscled inside for hard-earned layups.

With Georgetown missing back-to-back layups, Elon reeled off eight unanswered points to take a 13-10 lead.

Less than nine minutes in, Georgetown had allowed five three-pointers by four Elon players and trailed 19-18.

Both starting guards struggled with their shooting for a second consecutive game: Starks 0 for 4; Smith-Rivera, 1 of 6. Meantime, Elon scored at will, taking a 31-25 lead with 4 minutes 54 seconds remaining in the first half.

Starks finally got on the scoreboard on the free throw line, then hit his first three-pointer of the night to reclaim the lead for Georgetown, 34-33.

But Elon’s Troutman countered with tough-nosed plays, driving for baskets against the bigger Hoyas and keeping his team’s possessions alive, thanks in part to Georgetown’s half-hearted rebounding.

With a chance to retake the lead as the clocked ticked down in the period, the Hoyas turned it over on a travel, and Elon took a 40-39 lead into the break, having shot 58 percent from the field to Georgetown’s 45 percent.

The restive crowd shouted, “Defense, Hoyas!” and “Pound it inside!”

As if on cue, Georgetown’s big men took the ball inside for three consecutive layups that jump-started a 14-5 run and put the Hoyas up for good.