Senior Colin Morse threw a complete game seven-hitter, striking out seven, and the Hornets touched up Pioneers starter David Stover for three runs in the first two innings to get the win.
In the second, Coach Kevin Anderson's club strung together two consecutive hits and a fielder's choice to start the frame to load the bases and set up a two-run inning. Nick Goode led off with a double to right center followed by a Robert Marcelle infield single.
Christian Rice, who finished 2-for-4, drove in Goode with a single through the left side and advanced Marcelle to second.
Henry Delavergne, bunting for a sacrifice, laid one down the third base line that Brewer elected to go to third base with but was too late to cut down Marcelle.
Thompson then hit into a double play on a ball up the middle that brought Marcelle home with what proved to be the game-winning run.
Morse, who threw 90 strikes in his 131 pitches, now had enough offense to secure the win.
The right-hander faced the minimum through the first 4 2/3 and walked just one batter (along with one hit by pitch) to throw his first complete game of the season.
The Pioneers (27-17) scored a run on two hits in the sixth and one on walk, a hit and a sacrifice fly in the seventh.
In the eighth and ninth, Marietta put the tying run in scoring position only to see Morse get out of it with a 4-6-3 double play and a groundout, pop out, respectively.
"What a baseball game," Anderson said. "Two good teams that went after each other.
"Colin (Morse) was the story of the game. What a performance – he threw basically two pitches (fastball and slider) and only walked one batter.
"This is huge to get a win in the opening game. If you lose the opening game and look at the bracket, you have to win five or six games to win the tournament. I am not sure that any team has that kind of pitching depth because of the 25-man roster. We are going to face a good team tomorrow and hopefully we can continue to play good baseball."
Shenandoah, which has qualified for the NCAA regionals nine times (2009-12, 2014-present), has won its opening game each time.
Notes: SU is now 2-0 lifetime versus Marietta and has won both games by a 3-2 score... Shenandoah now won eight straight with five of the last six coming as a the away team and all five in the red uniforms... The Hornets are now 12-4 in the red uniforms...