Stephen Brett kicked three early penalties for the hosts to put Bayonne 9-0 in front after the opening 20 minutes, but Wilkinson cut the deficit with a penalty and a drop goal before half time, then levelled the scores soon after half-time with another shot at goal.
Toulon then pressurised Bayonne into errors late on, and Wilkinson landed two penalties in the final 12 minutes to secure a win which returned Toulon to third place in the table.
Racing Metro slump to defeat against Begles
France scrum-half Tillous-Borde extends Toulon deal
All Black Conrad Smith moving to France after World Cup