Former New Zealand lock Hoeata was dismissed for dangerous play as Agen pushed for an early try, with the hosts taking full advantage to claim back-to-back wins for the first time this season.
Despite going down to 14 men early on, tries from Louis Picamoles and Jesse Mogg sent Montpellier ahead.
Tamaz Mchedlidze and Johann Sadie closed the gap before a yellow card for Paul Willemse further enhanced Agen's numerical advantage, Jake McIntyre and Filipo Nakosi punishing the visitors' indiscipline with another two scores.
A penalty from McIntyre restored their nine-point lead after Joe Tomane crossed, with Montpellier unable to push on for a win after Aaron Cruden converted Romain Ruffenach's 71st-minute try.
Racing 92 closed the gap to Montpellier to just three points with Brice Dulin and Marc Andreu dotting down in a 17-13 victory over Brive.
Lyon got back to winning ways with the boot of Mike Harris seeing them past Toulon 15-6, Pau moved up to fourth with a 29-27 victory over Castres and Toulouse overcame Bordeaux-Begles, which had Thierry Paiva sent off, 25-19.