Neale Cooper's team went into the game with goalkeeping coach Paul Crichton making his Gills debut between the sticks because of injuries.
The home team made a bright start to the game and almost went ahead after just three minutes, when Michael Flynn failed to capitalise on Yeovil keeper Chris Weale's fumble.
The visitors then began to take control thanks to some excellent link-up play by the impressive Lee Johnson. Defender Efe Sodje came closest to breaking the deadlock on 18 minutes when his header cannoned back off the bar.
Pablo Bastianini had the best chance of the half, but he miscued his shot well wide from just six yards out.
The lively Matthew Jarvis responded immediately at the other end moments later, but his stinging drive from 12 yards was parried by Weale.
Neither side came out strongly after the break as the game failed to find its rhythm. Flynn was booked for a dangerous tackle on Bastianini, but Colin Miles' free-kick went straight at Crichton.
The game reached boiling point after 71 minutes when substitute Ashikodi received two bookings in the space of five minutes.
The first came after his attempted overhead kick struck Terry Skiverton in the face while the second left the Yeovil captain writhing in agony after the West Ham youngster appeared to stamp on him on the ground.
Steve Thompson's men then piled on the pressure with Phil Jevons coming closest with an acrobatic effort from close range, but they could not snatch the three points.