The final basket of the run was also the most dramatic. Levi Randolph swiped a pass near midcourt and fired it to Lacey under the basket. Lacey found a driving Retin Obasohan for a dunk.
It was the first tight game during Tulane's winning streak with the first three victories coming by a collective 69 points.
The Tide led 25-20 at halftime, holding Tulane to three points below its previous first-half scoring low. The Green Wave was just 7-of-25 shooting (28 percent) in the half.
Tulane solved some of its offensive problems in the second half, going 11 of 25 (44 percent).
This was a rare meeting in a once regular rivalry. It was the 84th time Tulane and Alabama have played but the first since 1998.