Congressman Ron Barber, who was up by about 4 percentage points, delivered a triumphant speech at the Democratic Party's celebration.
"We're ahead now and we're gonna win this race," Barber said.
Barber was in a rematch against Republican Martha McSally, who lost to Barber by just 2,500 votes in 2012.
An unknown number of votes remain to be counted, but Barber was leading by about 5,000 votes.
Barber took the stage as the crowd chanted his name.
"We said from the start that this campaign was going to be about issues and about policies and not about personalities," Barber said. "We took the high road, not the low road."