Owain Fon Williams outfoxed Liam Sercombe in an early one-on-one and the goalkeeper was relieved to see David Noble's dipping volley fly over the crossbar later in the half.
At the other end, Ben Hamer was kept busy as he saved shots from Gary Jones and Chris O'Grady, while Dale frontman Liam Dickinson's goalbound effort was blocked by James Dunne. Craig Dawson headed Brian Barry-Murphy's corner over the top.
The hosts appeared to be taking charge when they were hit on the counter-attack. Hamer's goal-kick was flicked on by Richard Logan, with the ball bouncing over Marcus Holness and presenting Cureton with a clear run at goal. He nicked the ball over Fon Williams to hand Exeter a 29th-minute lead.
O'Grady set up Jones for Dale's best chance of the half but the skipper blasted wide with a clear view at the target, while Exeter should have scored a second when Fon Williams spilled a Noble shot and the ball ran to Logan who wastefully hammered over the top.
Hamer was down quick at his near-post to keep out O'Grady's shot in the 53rd minute, while Jason kennedy cleared another Noble effort off the line after 74 minutes, although second-half chances were few and far between.
Source: PA
Source: PA