Francois Zoko also looked sharp in the opening spell for Stevenage, but curled his shot from the edge of the box just wide.
Zoko also looked to create chances for Jordan Burrow and Akins later in the opening 45 minutes, but neither was able to find the back of the net.
Stevenage continued to look bright at the start of the second half, as Obeng and Akins both applied pressure inside the box, but were unable to break the deadlock.
Callum Wilson managed to get the better of a couple of Stevenage defenders but Ashton was able to make another block to protect the visitors' goal.
The Sky Blues finally managed to secure the first goal of the night in the 67th minute when the visitors failed to mark Dan Seabourne during a Coventry corner, allowing the defender to head in.
The home side had a chance to double the lead and put the win beyond doubt with just five minutes left to play when they were awarded a penalty after Bira Dembele was adjudged to have handled the ball.
However, Steven Arnold correctly guessed where Wilson was going to put his spot kick, and made the save to give Stevenage the chance of rescuing a late point.
Stevenage hit the woodwork again late on, but were unable to find the back of the net before the full-time whistle.