Tony Mitchell added 15 points and freshman Nick Jacobs chipped in 13 in his first start for the Crimson Tide (8-2), who returned to a more characteristic defensive form after losses to Georgetown and at Dayton.
Detroit (5-7) 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.
Green made 7 of 9 shots from the field and 7 of 8 from the free throw line for the Tide.
Alabama had allowed a season-high 74 points and 61 percent shooting at Dayton, but played much stouter defense from the start in this one.
Detroit missed its first 11 shots and had only one point in the opening 6:47.
In Memphis, Tennessee, Donte Poole hit a career-best six 3-pointers and scored 20 points to help Murray State remain one of only nine teams in Division I that are still unbeaten.
The Racers (10-0) took control early then had to weather a late Memphis rally to hold on for the victory. Murray State was up 71-60 with just under 2 minutes left before Memphis (5-3) scored eight straight points to make it a one-possession game.
The Tigers trailed 73-72 with 14 seconds left, but Isaiah Canaan, who had 15 points, connected on two free throws with 7.9 seconds to go.
Will Barton led Memphis with 27 points on 10-of-13 shooting and Joe Jackson had 20.
D.J. Richardson scored 20 points to lead four players in double figures as Illinois remained one of nine undefeated teams in the nation.
After Illinois jumped out to a 17-point lead in the opening minutes of the second half, Coppin State went on a 20-5 run to cut the lead to 59-57. From there, Illinois responded with a four-guard lineup that provided enough offense down the stretch to seal the win.
Meyers Leonard had 18 points and 11 rebounds, and Sam Maniscalco and Brandon Paul each scored 12 points for the Illini.
Tony Gallo scored 21 points for Coppin State (3-5), which made 10 3-pointers.
