Wasps returned to the top of Pool 3 of the European Challenge Cup with victory in their 100th game in Europe.
Sam Jones ran in a sixth-minute try and Nick Robinson's accuracy with the boot gave the hosts a 13-3 lead after half an hour.
With Riki Flutey sin-binned, however, Sione Lauaki crossed to bring Bayonne to within two points at the break.
But Elliot Daly hit a 60-metre penalty and Robinson added three more kicks as Wasps sealed the win.
The only disappointment for the London side was the loss of captain John Hart, who hobbled off in the 19th minute.
The French side, who beat Wasps 19-11 last Saturday, are now a point behind them with two group games to go.
Wasps: Southwell; Haughton, Daly, Flutey, Wade; Robinson, Simpson; Payne, Webber, Broster; O'Donoghue, Wentzel; Birkett, Jones, Hart (capt).
Replacements: Lindsay, Taulafo, Castex, Burton, Harris, Davies, Davis, Waldouck.
Bayonne: Heymans; O'Connor, Lacroix, Mazars, Rokocoko; Boyet, Garcia; Iguiniz, Roumieu, Tialata; Linde (capt), Boutaty, Marmouyet, Puricelli, Lauaki.
Replacements: Da Ros, Manukula, Avril, Flavell, Baget, Phillips, Gerber, Otazo.
Referee: Neil Paterson (Scotland)