The Grecians struggled in the first half but took the lead just before half-time through Bertie Cozic. Dwayne Jackman equalised after the break before Exeter ran away with the game with goals from Matthew Gill, Lee Phillips and a late Billy Jones penalty.
Lee Clarke pulled a consolation goal back in injury time but by then the game was well beyond the visitors.
Exeter made two changes from the weekend draw at Gravesend, Jon Richardson coming in for injured skipper Chris Todd and Dean Moxey replacing Jon Challinor, who dropped to the bench.
St Albans, who had lost three of their last four league games going into the match, gave a debut to Jackman who was signed from Bishop's Stortford at the weekend.
A poor opening was littered with free-kicks and there were few chances at either end although stand-in Exeter skipper Phillips headed Andy Taylor's corner past the post.
At the other end St Albans forced a string of early corners but couldn't turn their early possession into chances. Paul Hakim tried his luck with a shot from the edge of the box but his effort was comfortably saved by Martin Rice.
Exeter were poor in the first half against their part-time opponents. Rob Edwards headed over from another Taylor corner but the Grecians offered little as an attacking force in the first period.
Exeter picked up three yellow cards as Danny Woodards, Billy Jones and Edwards all let their growing frustration boil over.
Matthew Gill shot wide from 30 yards as Exeter began to push forward but they never troubled Paul Bastock's goal.
Exeter were dreadful for 40 minutes but finally woke up just before half-time. Cozic had the first shot on target for the Grecians with a fierce shot after a fine run which was well saved by Bastock. Taylor was then picked out by Phillips and his shot from 15 yards was again pushed away by Bastock.
Exeter finally took the lead two minutes before the break with the best move of the half. Gill picked out Phillips who broke well down the right, and when his low cross was cushioned by Jamie Mackie, Cozic swept the ball home from 12 yards.
Exeter hardly deserved to be ahead at the break but at least produced a goal to remember in an otherwise forgettable first half.
The game opened up after the break and there were early chances at either end. St Albans started brightly and Clarke's powerful half-volley from the edge of the box was well saved by Rice.
Exeter could have stretched their lead when Cozic and Mackie exchanged passes inside the box but the Frenchman scuffed his shot wide from six yards.
Taylor then picked out Mackie with a fine cross but his header was comfortably saved.
St Albans stunned St James Park with an equaliser against the run of play. Jackman charged down an attempted clearance by Edwards and darted into the box before stroking the ball past Rice.
But the Grecians restored their lead less than 10 minutes later. Taylor's cross found Phillips who set up Gill, and the midfielder rifled the ball home from 18 yards.
The visitors were almost level within a minute. The ball was threaded through to Jackman and the striker twice had shots blocked by desperate lunges as Exeter were stretched at the back.
Exeter looked a much better side after the break. Phillips had a shot comfortably saved from 35 yards before the striker put the game beyond doubt with nine minutes left on the clock.
Phillips was picked out by Moxey's cross and the striker controlled the ball with his chest, took it past a defender and thumped it home from 10 yards.
In the dying minutes Tom Davis tripped Mackie inside the box and Jones thumped home the resulting penalty.
In injury time Clarke stretched to reach a deep cross and tapped the ball home at close range with almost the last kick of the game.