The sophomore pitcher threw eight shutout innings, but that wasn't enough to get the win as WSU's Ryan Walker countered with seven of his own shutout innings.
In fact, neither team scored a run until the 11th inning.
Kevin Newman was hit by a pitch and Dalbec was intentionally walked to bring Casey Bowman up to bat with two on and two out.
This was just Bowman's second at bat of the season, who was put in at third base after several lineup changes in the late innings to accommodate Dalbec.
Bowman worked a seven-pitch at bat before flying out to center.
Except the centerfielder dropped the ball, and both Newman and Dalbec scored, giving Arizona a 2-0 lead.
Tyger Talley, who was on his third inning of work, made it interesting in the bottom half of the 11th, loading the bases before inducing a ground ball to end the game and give Arizona the 2-0 victory.
The win allowed the Wildcats to take the series, despite only getting four hits on Sunday. They improve to 27-18 overall, and are now 11-13 in Pac-12 play. Arizona hosts Washington next weekend in the second-to-last conference series of the season.