Rio Hardy’s late goal wrapped-up a first win of the season for the Red and Green, despite the Wildcats spending large spells of the game camped-out in the hosts half.
United could have been ahead with barely two minutes on the clock as Dee Bradley prodded wide following Beth Hepple’s free-kick.
Megan Borthwick did have to come out and smother a couple of long balls as Coventry looked to get in behind, but in truth neither goalkeeper was seriously tested during the first-half – although Lucy Thomas in the home goal did have to leap to gather a goal-bound cross from Lily Crosthwaite.
It was still the Wildcats seeing more of the ball as the half wore and they had a glorious chance to take the lead when Beth Hepple dinked a ball to the back post, but neither Danielle Brown or Bridget Galloway could find the telling touch.
Brown came close once again before the break but found the side netting from a tight angle, while Mollie Lambert had a near-identical chance moments later which resulted in the same outcome.
Durham introduced Emily Roberts at the halfway mark in a bid to find an elusive goal, and the change almost brought an immediate reward.
After cutting in from the flank, the winger saw her curling effort spectacularly kept out of the top corner by Thomas.
But while Durham were still dominating possession, Coventry were a threat on the break. And a quick counter almost yielded an opener as Katie Wilkinson swept a shot against the bar after Borthwick had attempted to dispossess Hardy.
Wilkinson came close again from the resultant corner as she headed narrowly wide, before the visitors again set about imposing themselves on the game.
Galloway saw a shot blocked by Mollie Green before Roberts drilled wide from the edge of the area.
The Wildcats came agonisingly close to an opener with 15 minutes remaining as Sarah Robson saw her glancing header from a corner strike the bar.
Set pieces were a real source of opportunities for Durham and, with five minutes on the clock, Thomas looked to have fumbled one of the deliveries into her own goal – only for the officials to adjudge that the ball hadn’t crossed the line.
And seconds later, Coventry took the lead.
It was a fine finish from Hardy, who found the top corner from inside the area.