The Crimson Tide (14-11, 4-7 Southeastern Conference) rallied from a 13-point deficit early in the second half to snap a four-game losing streak.
The Razorbacks (13-12, 6-4) had won five straight games to take the SEC West lead but couldn't finish this one out. Courtney Fortson made 1 of 2 free throws with 36 seconds left to cut Alabama's lead to 67-66.
Arkansas quickly fouled Mikhail Torrance who, like Green and Brock, made both shots from the line.
The Razorbacks' only basket in the final 2 minutes came on Fortson's drive with 8 seconds left. Brock then secured the victory from the line.
Green had 22 points and nine rebounds and made all but one of his 13 free throw attempts.