The hosts scored the only goal after seven minutes when a poor clearance by goalkeeper Lee Burge fell to Harley 25 yards out and his lobbed effort went in off the upright.
Coventry responded with a Jack Grimmer shot that was easy for Christy Pym, while Exeter striker Jayden Stockley was just off target with a fine shot from distance.
Harley saw another goalbound effort blocked and as Coventry countered, Pym stood up well to beat away Marc McNulty’s effort.
Coventry’s best chance fell to Maxime Biamou, who was played in on goal, but Pym again stood up and saved well to preserve Exeter’s lead.
McNulty almost capitalised on a Troy Archibald-Henville error, but was denied by Pym, before the striker saw another effort deflect over the bar.
Substitute Jordan Ponticelli clipped the top of the crossbar in stoppage time for Coventry, but the Sky Blues could not force an equaliser and are now eighth, one point below their opponents.
Southampton manager Mark Hughes was delighted to see his new side reach the FA Cup semi-finals but also warned that the Premier League remains a concern.
Borussia Dortmund winger Andre Schurrle was delighted with the team's hard-fought 1-0 Bundesliga victory over Hannover 96 on Sunday afternoon.
Chelsea defender Andreas Christensen has revealed that he sought advice from club legend John Terry after making a few costly mistakes recently.