Woodward (5-1) held the Blazers to three singles and struck out seven batters in seven innings of work. He wriggled out of the only UAB threat in the second inning after allowing back-to-back one-out singles to Matt Gaulden and Seth Rollin. A wild pitch moved both runners into scoring position, but Woodward struck out Joe Yarbrough and got Mark Garner on a pop up to second base.
"Woodward pitched really well tonight," Alabama head coach Jim Wells said. "That was a nice comeback after a rough outing last week at Jacksonville State. He had good command of all hit pitches and threw a change up to the left handed hitters.
After that, the Blazers never mounted a serious threat against the right-hander, who also beat UAB on April 10 at Young Memorial Field.
Woodward pitched around a two-out error in the fifth inning. In the seventh, he pitched around a lead off single and error, by striking out two batters and retiring the third on a stolen base attempt.
"That is as good as he has pitched in a long time," Wells added. "He did a great job tonight."
Alabama, winners of five straight games, scored single runs in the first and second inning to take a 2-0 lead. In the first inning, Adam Pavkovich reached on an error by UAB second baseman Seth Rollin and moved into scoring position on Jeremy Brown's single to center. Brent Boyd followed with a bloop single down the right field to score Pavkovich with the first run of the game.
The Crimson Tide made it 2-0 in the second inning when Travis Garner doubled with one out and scored on Scott McClanahan's two-out double to right center field.
Alabama (39-7) doubled its lead to 4-0 in the fifth inning with two more runs off losing pitcher Andre Parks. McClanahan walked and scored on Pavkovich;s double down the left field line. Pavkovich later scored on a throwing error by UAB shortstop Mark Garner to give the Crimson Tide a 4-0 lead.
Pavkovich's RBI double extended his career high hitting streak to 12 games. It is also the longest by an Alabama player this season.
Parks (2-9) allowed four runs on eight hits in 4 2/3 innings. He added two walks and two strikeouts.
Alabama pulled off a baseball oddity in the sixth and seventh innings by scoring a run in each inning with the benefit of a hit or a Blazer error.
In the sixth inning, Garner drew a one-out walk before stealing second and third base. Marshall's sacrifice fly to right field, scored Garner to give the Tide a 5-1 lead.
In the seventh inning, Stonard and Brown drew back-to-back walks to put runners at first and second base. Boyd's fly ball to right field moved Stonard to third base with two outs. Brown and Stonard then executed the double steal, allowing Stonard to cross the plate with the Crimson Tide's sixth run.
UAB (14-30) avoided the shutout when Mitch Jones hit a solo home run with two outs in the eighth inning off Brent Carter. Carter allowed one run and one hit in two innings, adding two strikeouts.
Jones' solo home run snapped a streak of 21 2/3 consecutive scoreless innings by the UA pitching staff over three games. UA had not allowed a run since the fifth inning of Saturday's 6-5 win over Auburn. Woodward and Carter also combined for nine strikeouts against the Blazers, giving the staff 21 strikeouts in the last 18 innings.
Alabama capped the scoring in the eighth inning on a two-run single by Pavkovich. Marshall doubled and moved to third on McClanahan's base hit to left. Both runners scored on Pavkovich's second hit of the game.
Marshall, making his second straight midweek start behind the plate, had two hits and one RBI. Pavkovich had two hits and three RBI to lead the UA offense. McClanahan added two hits, scored two runs and drove in one run for Alabama. Brown reached base all four times, collecting two hits and two walks.
Alabama will travel to Athens, Ga., this weekend for a three-game set with the Georgia Bulldogs. The series opener is Friday, May 3 at 6:30 p.m. (ET). The teams play Saturday and Sunday at 2 p.m. (ET). UAB travels to Ft. Worth, Texas for a three-game series at TCU.