Exeter took the lead in the ninth minute with a well-worked goal. Paul Buckle won the ball in midfield and, when it was knocked out to Billy Jones, his perfect cross was headed powerfully into the top corner.
The lead lasted ten minutes before Altrincham pulled level in bizarre circumstances. Stephen Aspinall's hopeful ball forward should have been collected by goalkeeper Paul Jones but he spilt it into the path of striker Colin Little who fired home into the empty net from eight yards.
Exeter continued to probe without looking particularly dangerous but they regained the lead just before the half-hour mark.
Matthew Gill's long throw found Jamie Mackie who leapt well to nod the ball home from six yards.
The visitors could have pulled level when Peter Band picked out Little but the striker fired inches wide from 12 yards.
Altrincham were reduced to ten men on the stroke of half-time when defender Mark Maddox was shown red after kicking out at Mackie.
Exeter stretched their lead and effectively put the game beyond any doubt seven minutes after the restart. Lee Phillips darted into the box and whipped in a fine low cross which was converted at close range by Jon Challinor at the far post.
Phillips then headed over from Andy Taylor's fine cross and saw another cleared off the line by Christian Adams.
Substitute Colin Potts had a header cleared off the line for Altrincham in the closing stages but it was too little too late.
Exeter boss Alex Inglethorpe said after the win: "I think we've shot ourselves in the foot in recent weeks and we haven't given ourselves the best chance of getting into the play-offs.
"But that said if we keep playing like we did today then who knows."