With an hour gone, Andy Dawson’s cross from the left found Evans who rifled in a volley to give the Tigers a third consecutive victory which lifted them to fifth in the Championship.
Coventry created few meaningful chances but were unlucky not to go in front in the first half when Richard Wood’s header hit the post.
For all their effort in the second half the Sky Blues were unable to find a way through and have now gone 10 matches without a win.
Coventry boss Andy Thorn made three changes to his side with Cody McDonald, Conor Thomas and Gary McSheffrey coming in for Clive Platt, Gael Bigirimana and Sammy Clingan.
Barmby kept faith with the same side from the home win over Birmingham on Wednesday, with fit-again Richard Garcia replacing Dele Adebola on the bench.
Neither side imposed themselves in the early stages but the first chance fell to Hull, with Aaron Mclean heading wide from Dawson’s cross.
Coventry had barely threatened and their only moment of note in a dour first half-hour came when McSheffrey played a clever reverse pass to Richard Keogh and his dangerous ball into the box was scrambled away.
That chance woke Hull up and they broke up the other end with Cameron Stewart forcing Coventry goalkeeper Joe Murphy into a decent save.
The game began to open up and Coventry midfielder Carl Baker tested Peter Gulacsi before Mclean had a shot blocked by Nathan Cameron.
Ten minutes before the break Coventry came agonisingly close to going in front when Thomas’ cross found Richard Wood and his header thumped against a post.
Hull tried to make the most of that let-off and Robert Koren tried his luck from distance twice before the break but was off target on both occasions.
The Tigers continued where they left off at the start of the second half and Stewart did well before firing in a shot from 20 yards which flashed wide.
Wood sent a header wide for Coventry before Hull went ahead on the hour mark when a good move on the left ended with Dawson putting in a looping cross which Evans volleyed in.
Coventry immediately went in search of an equaliser and Gary Gardner fired over from 20 yards before Thomas had a shot parried by Gulacsi.
But Hull still looked the side with a greater cutting edge and Mclean got into the box and his cross-cum shot flashed across goal.
Coventry rallied late on and Lukas Jutkiewicz had a shot saved by Gulacsi before heading wide from a Keogh cross as Thorn’s side slumped to a third consecutive defeat.