Yeovil had already taken a first-half lead after 36 minutes when midfielder Keiran Murtagh met a left-wing corner with a perfect volley - giving Wanderers' goalkeeper Scott Shearer little chance.
In the second half Wycombe had their chances to equalise but were denied by some superb saves from Yeovil's on-loan keeper Alex McCarthy.
Obika made an immediate impact in the 70th minute when he collected a quick throw-in and crossed from the left for JP Kalala to apply the finish from close range.
Two minutes later it was Obika's turn to score. He burst through the defence, timing his run perfectly and shooting past Shearer. The final goal was created by Obika's fellow substitute Andy Welsh who provided the cross for Sam Williams to produce another routine finish for Terry Skiverton's side.