With more than half the precincts reporting in the state's largest district, Rodriguez had 57 percent to Bonilla's 43 percent.
They were the top vote-getters in a special election held Nov. 7, but neither got 50 percent, prompting the runoff.
Bonilla was seeking an eighth term in Washington, while Rodriguez was hoping to return after a two-year absence. He served from 1997-2005 in another district but was ousted in the March 2004 Democratic primary by Henry Cuellar, a Laredo Democrat. Rodriguez lost again to Cuellar in this year's primary.
The Supreme Court ruled in June that a 2003 reconfiguration of Bonilla's district was unconstitutional because it diluted minority votes, and a three-judge panel redrew the district in August to restore Hispanics that had been shunted into another district.
The new district, which stretches from San Antonio south to the Mexican border and almost to El Paso in the west, gave Rodriguez yet another chance at national office and made Bonilla fight a little harder to keep his seat.
Rodriguez, Bonilla and six others ran in a free-for-all special election Nov. 7. The goal of the six Democrats was to keep Bonilla below 50 percent and force him into a runoff. It worked, with Rodriguez in second place.