The Titans missed three shots the first time down the court, two on the second and plenty more after that.
Green scored 21 points and the Crimson Tide went back to its stingy ways in rebounding from a two-game losing streak with a 62-54 victory over Detroit on Sunday night.
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"It was a point for us to come and jump on them early," Green said. "Coming back from the last game, we didn't defend at all and that's why we lost."
Tony Mitchell added 15 points and freshman Nick Jacobs chipped in 13 in his first start for the Tide (8-2), which returned to a more characteristic defensive form after losses to Georgetown and at Dayton.
Alabama had allowed a season-high 74 points and 61 percent shooting against Dayton, but played much stouter defense from the start in this one.
Detroit (5-7) missed its first 11 shots over nearly the opening 7 minutes.
"The last two teams came in and they punched us in the mouth," Mitchell said. "We just wanted to come out and be the one to punch them in the mouth.
"The stuff we usually do, we just wanted to get back to that, just play great defense and get out and run."
They still couldn't run away with the game.
Detroit trailed by 22 points late in the first half and failed to approach its 75.9-point scoring average. The Titans shot 32 percent (17 of 53) and missed all 12 3-point attempts.
"I was disappointed in our slow start," Detroit coach Ray McCallum Sr. said. "Alabama had a lot to do with it. They came out focused and got us back on our heels.
"It took us a while to settle down and find a rhythm. We got caught up playing their game."
Green made 7 of 9 from the field and 7 of 8 from the free throw line for the Tide. Mitchell also had eight rebounds and four dunks, three on alley-oop passes.
Detroit's Ray McCallum Jr. scored 13 points after going into halftime without making a field goal, while Doug Anderson added 12 and Chase Simon had 10 on 2-of-11 shooting.
Lamarcus Lowe was only 1 of 7 from the field for four points but also grabbed 10 rebounds.
"I felt like as always it had to start for us on the defensive end," Tide coach Anthony Grant said. "I felt like this was a very dangerous team walking into our building.
"We knew the challenge walking in and I thought our guys came out, especially in the first half, with great intensity, great focus, great unselfishness."
Alabama opened its biggest lead late in the first half before Detroit finished with six straight free throws to start a 19-6 run extending well beyond halftime.
Green and Mitchell combined to outscore the Titans by a point in building a 38-22 halftime lead as the Tide held its sixth opponent in the first 10 games below 25 points in the first half.
The Detroit spurt cut it to 44-35 9 minutes into the second. Alabama had four turnovers and two ugly misses on consecutive possessions before cleaning up its act.
Green made 3 of 4 free throws with Anderson drawing his fourth foul on a technical, and then Mitchell hit a 3-pointer from the top of the key.
The elder McCallum wasn't sure what sparked the official's call in front of Alabama's bench.
"I never did get an explanation," he said. "It was a momentum swing for them. I didn't see anything and my player said he didn't do anything."
Added Grant, "I don't know what the technical foul was for."
The Titans didn't push it back into single digits until Anderson's putback with 1:08 left but they couldn't get any closer.
The 6-foot-8, 250-pound Jacobs gave Alabama a bigger starting lineup in replacing fellow freshman Rodney Cooper. He blocked a couple of shots but didn't have a rebound.
"I felt like Nick earned it with what he's done on the practice court and being able to transfer that to the game," Grant said. "I thought he brought a physicality and a presence down low. I thought he did a pretty good job on the defensive end."