The visitors, beaten only once on their travels this season, snatched the lead against the run of play 11 minutes before the break with their first chance. Midfield man Liam Sercombe drilled home an excellent right-foot shot from the edge of the box from a chance set up by John O'Flynn.
It came after the Iron had squandered multiple chances in front of goal for the second successive home game.
The best fell to striker Deon Burton, still looking for his first home goal, but after breaking free into the box his shot failed to beat goalkeeper Artur Krysiak.
Scunthorpe needed to step up the pace in the second half but it was Exeter who struck again with two goals in two minutes to climb to joint top spot in League Two.
The first was a wonder strike from midfield man Arron Davies, who swivelled and hit a tremendous right-foot shot from 35 yards that dipped over keeper Sam Slocombe and into the net after 48 minutes.
Then it was Sercombe who struck again, tucking his shot inside the far post from a low-right wing cross from Davies.
Substitute Sam Parkin made it 4-0 for Exeter in the 90th minute with a good individual effort.