Delaware played its third straight game without first team All-America Elena Delle Donne, who is suffering from Lyme disease symptoms.
Trailing most of the game, Delaware (1-2) fought back in the second half, and Lauren Carra's jump shot with 11:38 to play tied the game at 33.
Delaware took the lead, 44-43, after Stephanie Leon's jumper with 3:59 remaining, but Duquesne (2-1) answered.
April Robinson's layup with 3:19 to play recaptured the lead for Duquesne, 45-44, and they never trailed again.
Danielle Parker's two free throws cut the lead to 48-47 with 45 seconds to play, but Szecsi made a 3-pointer with 19 seconds left to seal the victory for Duquesne.
Szecsi finished with seven points.
Carra finished with 12 points and 6 rebounds for the Fightin' Blue Hens, and Danielle Parker added 11 points and eight rebounds.
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