Hunt, who put the nightmares of his clash with Petr Cech behind him in a man-of-the match display against Chelsea in midweek, was Reading's hero in a tight game against David Moyes' UEFA Cup qualifiers.
He made the breakthrough right on half-time, ghosting in to space in the penalty area and flicking a neat finish beyond Tim Howard in Everton's goal.
After holding champions Manchester United to a creditable draw at Old Trafford and then narrowly losing out to Chelsea in midweek, Reading's start to the season hardly got any easier with the visit of early Premier League pacesetters Everton.
The Toffees came to the Madejski Stadium on a high after back-to-back wins as they looked for a repeat of their 2-0 win in the corresponding fixture last season.
And they looked destined to make an early breakthrough when Mikel Arteta pulled the ball back for Andy Johnson eight yards out, only for Andre Bikey to make a brave block and save a certain goal.
But, that 11th minute scare aside, it was Reading who dominated the first half, though they rarely threatened Howard's goal.
Kevin Doyle did force the American keeper to stretch himself and the home side were unfortunate not to win a penalty when Joleon Lescott appeared to lean into Shane Long's deflected cross shot.
But the home side made a deserved breakthrough on the stroke of half-time when substitute Ulises De la Cruz's throw saw Doyle out-muscle Alan Stubbs, allowing Hunt to run into the space behind and control neatly with his thigh before angling a shot beyond the reach of Howard.
The tight exchanges continued in the second half with Reading dominating possession but struggling to create any real clear-cut chances.
Everton found openings even harder to come by, though they were nearly gifted an equaliser was when Marcus Hahnemann punched an Arteta free-kick against Bikey and was relieved to see the defender keep his cool and stroke the ball to safety.
Hahnemann did well to beat away a fierce cross shot from substitute Steven Pienaar and, when the keeper was beaten late on, he was grateful to see his woodwork twice come to the rescue.
James McFadden, moments after being booked for a ludicrously ambitious dive in the penalty area, bent a clever effort beyond the keeper but against the frame of the goal.
Johnson was on to the rebound in a flash but saw his first effort blocked by Hahnemann and then the rebound bounce back off the post again as the striker wasted the best chance yet to snatch a point and open his account for the season.