"Richardson is a phenomenal city, and I cannot wait to serve as city councilwoman," DePuy wrote on Facebook.
Votes from all 28 precincts show DePuy edging out a narrow win, with just 82 more votes than her opponent Dan Barrios. By night's end, DePuy had garnered 51.06% of ballots.
DePuy declared her victory via Facebook. She could not be reached for further comment.
Barrios said he would take the experience of running for council "to the grave" and was "deeply humbled" by the support for his campaign.
"I will never forget the people I met at the doorsteps," he said. "... I will continue to serve in any way I can."
DePuy and Barrios collected more votes than opponent Franklin Byrd in the May 6 general election. The pair headed to a runoff when neither garnered 50% of the vote.
DePuy will be the only woman on the seven-member council. She fills the seat vacated by outgoing council member Scott Dunn.