Substitute Jayden Stockley struck a last-gasp winner as City saw off Barnet at The Hive.
The Grecians fell behind shortly after the interval - Shaquile Coulthirst turning past Christy Pym at the near post - but the visitors bounced back, first through Reuben Reid before Stockley's first goal since his return secured all three points in the Capital.
Paul Tisdale named an unchanged starting XI for the third game running as City looked to stretch their three-point lead at the summit.
It was the visitors who started the brighter at a rain-sodden Hive; Liam McAlinden bending one over the crossbar with three minutes on the clock.
Despite City's slick play in the middle third it was Barnet who should have been ahead just before the quarter-hour mark. Jamal Campbell-Ryce's cross found Michael Nelson at the back stick, but Pym was at his best to save twice in quick succession from the barrel-chested centre-back.
McAlinden was presented with his second opportunity of the evening moments later, firing into the hands of Craig after a neat turn saw him advance into the area.
Pym was forced into action again on 20 minutes, palming Harry Taylor's long-range drive over the crossbar and into the contingent of travelling supporters behind the goal.
Exeter ended the half in the ascendancy as the rain continued to pour in the Capital. Jake Taylor - who has goal-scoring history at The Hive - saw an effort drop just inches wide of the post before McAlinden's strike deflected wide off Nelson.
Charlie Clough cleared the crossbar at the other end in the last action of a frantic first period.
Barnet took the lead just three minutes after the interval. A well-worked move down the right-hand side saw Campbell-Ryce advance down the right and square for Coulthirst who steered past Pym at the near post.
The Grecians were presented with a chance to equalise ten minutes later but Reuben Reid's heavy touch allowed Ross to sweep up following a super surge from McAlinden.
Pym was called into action twice in quick succession as Barnet went in search of a second, first denying Ricardo Santos from close range before diving low to his left to foil Santos again.
Boateng's introduction shortly after the hour-mark saw City wrestle back some control. James tested Ross with a shot from just inside the box after a clever dummy from Reid bought the Welshman some room to manoeuvre.
Lee Holmes' first-time cross found Jayden Stockley on 71 minutes but his towering header was comfortably claimed by Ross. Pierce Sweeney's header thumped the crossbar moments later as City continued to turn the screw.
Six minutes later and Exeter were back on level terms. Taylor's arrowed drive found the woodwork and it was Reid in the right place at the right time to slide home from five yards out.
But for Ross' acrobatics it would have been a second for City shortly after; the Bees keeper at full stretch to tip Troy Brown's header over the crossbar.
With the game in its dying embers Stockley provided the spark; the former Aberdeen man following up to score from close range to send the City fans into raptures.
Exeter City: Pym, Sweeney, Woodman (Stockley 66), James, Tillson, Holmes, Moore-Taylor, McAlinden (Boateng 61), Taylor, Reid (Moxey, 94), Brown.
Subs not used: Hamon, Archibald-Henville, Edwards, Sparkes.
Barnet: Ross, Clough, Santos, Nelson, Campbell-Ryce, Coulthirst, J. Taylor (Fonguck 80), Tutonda, H. Taylor, Vilhete, Akpa Akpro (Akinde 78).
Subs not used: McKenzie-Lyle, Bover, Shomotun, Mason-Clark, Smith.
Attendance: 1,605 (376 away)