Sean Devine grabbed a stunning hat-trick to sentence Burton to their third successive Conference defeat in a seven-goal thriller at Eton Park.
Burton cut the deficit three times, but ultimately paid the price for a nightmare start in which Devine rocked them with two goals in 12 minutes.
Burton dominated much of the game, but could not match Exeter's razor-sharp finishing, while the defensive frailties which have seen them leak ten goals in three games were fully exposed.
In fairness, there was little the home team could do about Devine's opening goal, a magnificent 20-yard left-foot volley after only two and a half minutes.
But the striker was given far too much room to attack the Burton defence in the 12th minute and punished them with a crisp low drive into the bottom corner from 12 yards.
Burton staged the first of their fightbacks four minutes later when Aaron Webster rocketed home a penalty after Andy Ducros had been barged over by Chris Todd.
Either side of the interval, Burton's persistent pressure seemed destined to put them on level terms but they could not finish off their clever approach work.
Exeter showed them how by re-establishing a two-goal lead in the 71st minute when Steve Flack pounced on a loose ball in midfield and broke clear to set up James Coppinger for a magnificent right-foot shot into the far corner from 25 yards.
Burton grabbed another lifeline a minute later when substitute Christian Moore arrived at the far post to head in Dale Anderson's cross.
But Exeter produced another devastating counter attack in the 82nd minute, Coppinger this time the creator with a superb pass that picked out Devine for a low shot inside Matt Duke's left-hand post.
In a thrilling climax, Webster stroked home his second penalty after a handling offence, but City rode out more late pressure to secure the points.