Mullin had nearly 56.5% of the vote compared to about 43.5% percent for San Mateo County Supervisor David Canepa, according to initial semi-official results Wednesday.
Mullin, 52, was elected to the Assembly in 2013 after serving on the South San Francisco City Council and is the son of former state Assembly member Gene Mullin.
Speier, who is retiring after nearly 15 years in Congress, endorsed Mullin, who worked for her when she was in the state Senate.
Canepa, who served eight years on the Daly City City Council before joining the county Board of Supervisors six years ago, congratulated Mullins following the release of the initial results Tuesday night.
"Running for Congress has been the most exciting year of my life and I'm so proud of my team. We fought hard and we never gave up. Congratulations to Kevin Mullin, we wish him the very best of luck and look forward to working with him on the most pressing issues our nation faces," Canepa said.