The 26-year-old Harrison's career has been slowed by injuries that have required surgery eight times, and he came into the tournament ranked No. 789. He has five ATP Tour match victories, with three of them coming in the past week. He also won two matches in qualifying.
"It feels pretty amazing," Harrison said. "I'm pretty even-keeled right now -- just happy to keep playing."
Harrison regrouped against Mager after losing serve in the first game, when he double-faulted twice.
The only lower-ranked semifinalist in Delray history was Juan Martin del Potro when he was making an injury comeback in 2016.