Bent rounded off a rare attack from the visitors by tapping the ball into an unguarded net seven minutes after the interval - it was Everton's only shot on target of the afternoon.
However, David Moyes' side deserved the points after producing a fine defensive display that stifled Bolton's unimaginative attacking play.
The Trotters relied far too much on the long ball to Kevin Davies and as a result failed to test visiting goalkeeper Nigel Martyn with any degree of regularity.
But in the closing stages the former England shot-stopper was required to produce a fine reaction save to tip El-Hadji Diouf's powerfully struck drive on to the crossbar.
The home side controlled the first half and Martyn had to rush from his line to prevent Davies getting a shot in, before Henrik Pedersen squandered two good chances.
Everton were forced into a reshuffle when Alessandro Pistone was stretchered off after half an hour, but looked more comfortable after Phil Neville dropped into the back four.
The home side started the second half strongly and Davies was presented with a good chance by Pedersen, but made a mess of his shot which dribbled through to Martyn.
Everton took a surprise lead in the 52nd minute with a move straight out of Sam Allardyce's book of tactics.
Duncan Ferguson failed to get his head to a long punt downfield but the combative striker's jump wrong-footed the home defence and the ball bounced through to Tim Cahill.
The Australian shaped to shot from a tight angle, but screwed his shot across the face of goal where Bent was waiting to prod it home.
The goalscorer hobbled off soon afterwards to add to Everton's problems ahead of their midweek trip to Villarreal, but at least Moyes had the satisfaction of seeing his defence hold firm.
Kevin Nolan blasted over when well placed before Martyn's crucial save to deny Diouf, but all too often Bolton's mis-placed passing and poor set-piece delivery made it simple for the visitors to hang on to their slender advantage.
Trotters boss Allardyce was furious with his players and complained: "We've now only got one point out of six and it's a struggle from here, we're already playing catch-up.
"We battered Everton from start to finish and dominated the game but a lack of quality let us down.
"The Premiership is cruel, it will punish you. We made one slip for one second and Everton scored.
"This was a perfect example of what happens when you do not take advantage of the chances you create. We had 17 attempts on goal to their three yet ended up losing the game.
"We were never under the cosh yet we ended up with nothing, it is so frustrating."
Moyes was relieved to see his side record their first win of the campaign and saw no reason to apologise for their defensive approach.
He said: "We defended well, it was a constant bombardment, and a good result for us. I thought our players all along the back four were superb."
"We were good enough to keep Bolton out and we got the goal that counted.
"You know when you come to Bolton it's going to be hard and we had to dig in to get the victory.
"You could count on one hand the teams who will come here this season and get the points, so we did very well."