Altrincham made the best possible start and took the lead after just 89 seconds following a neat move. Colin Little exchanged passes with Joe O'Neill and when Little's shot from ten-yards was blocked by Martin Rice Lawton was in the right place to stroke the ball home from close range.
Exeter began to push forward and defender Danny Woodards fired wide from long range after a fine run. The Grecians thought they should have had a penalty in the 15th minute. Adam Stansfield stole the ball from Peter Band, and as the striker scampered into the box and prepared to shoot he appeared to tripped by Band's lunging tackle as the defender attempted to recover. But the referee waved away Exeter's angry appeals.
The visitors should have made it two just before the half hour mark. Lawton cut the ball back to Little and the striker fired a shot past the post from ten-yards.
Exeter were level six minutes before half time. Billy Jones curled in a corner and Todd made no mistake with a bullet header from five-yards.
Stansfield and Mackie began to look a real threat for Exeter. Stansfield burst into the box and was denied by a lunging tackle. Mackie then headed narrowly wide from Challinor's fine cross. Exeter were well on top by now and brought on striker Lee Phillips as they hunted a winner.
Exeter struck the winner with five minutes left on the clock. Taylor's deep cross beat the defence and when the ball fell to Challinor he chested it down and struck a sweet volley past Coburn from 12-yards.