Huddersfield Town 1 Bournemouth 0
The Terriers were in danger of being dragged into a relegation scrap on the back of a run of five matches without a win.
But Jevons struck ten minutes from time and that proved enough to see off a poor Bournemouth side who offered little punch up front.
With places up for grabs in Town's FA Cup fifth round trip to holders Chelsea next month, the home side's performance was much improved on recent league outings.
Town had an early chance when Jevons beat keeper Gareth Stewart, only for Josh Gowling to clear off the line.
Jevons was Town's big danger and he had another effort on goal blocked. The impressive Malvin Kamara saw his follow-up blocked by Stewart.
Jevons fired over on the half-hour, but made no mistake five minutes later with what proved to be the winner.
Rob Page caused problems at a corner and Shaun Cooper and Russell Perrett went for the same header and only succeeded in setting up Jevons, who blasted into the top corner.
The Cherries only had one chance all game when keeper Matt Glennon pushed aside Cooper's free-kick.
Stewart kept Huddersfield at bay throughout the second half with key saves from Kamara and Luke Beckett.
Ten minutes from time a Beckett lob landed just wide and Jevons really should have sealed the points after that when Kamara gave him every chance to score from inside the box. The striker fired straight at Stewart.