Bolton lost to a Marcus Bent goal that came from Everton's only on-target effort and spent most of the second half, plus patches of the first, creating and squandering clear chances.
"We have been dealt a very cruel blow,'' said their disbelieving manager, Sam Allardyce. "Seventeen attempts at goal versus three, and we've lost. We can't keep a clean sheet, not even in pre-season, and, if that's the case, one goal won't be enough. Otherwise we won't finish in the top half.''
More than a little short-changed by a Premiership return of one point out of six, Bolton discover on Friday who they will play in the first round of their first European campaign.
Any foreign coach sent a tape of this one-sided meeting of last season's sixth and fourth-placed clubs will not relish a trip to the Reebok Stadium next month.
There was nothing about Bolton's performance, despite the result, to suggest they will be any more welcoming to their visitors in the Uefa Cup. Despite recruiting players from more than 30 countries in less than six years and currently having 19 different nationalities on his books, Allardyce remains pragmatic enough to insist that set-piece tactics deserve a prominent place in the football language.
Bolton were in Everton's faces almost throughout and Henrik Pedersen, Kevin Nolan, Gary Speed, Kevin Davies and Radhi Jaidi all spurned opportunities.
They must have known defeat was inevitable when the last in the long line was slammed against the bar three minutes from time by the impressive El-Hadji Diouf.
By the time Bolton's number comes out of the hat in Monaco in four days' time, Everton might have joined them in the Uefa Cup.
Perhaps Everton felt they were due a stroke of luck after the Champions' League pairing with the powerful Spanish side Villarreal and an unkind Premiership opener against Manchester United. They will hope they have not used up their quota here.
The safety net of a place in Europe's secondary tournament will accompany them when they go in search of a comeback against Villarreal on Wednesday but they will feel a weight lifted from their shoulders with this victory.
An off-target glancing header by Tim Cahill was virtually their only effort at goal before or after their 52nd-minute winner. The route by which they broke through was not untypical of Bolton's football.
Duncan Ferguson could not reach Joseph Yobo's long high ball down the middle but it ran on for Cahill to feed intelligently across Jussi Jaaskelainen's six- yard area and leave Bent with a tap-in.
Alessandro Pistone went off with damaged knee ligaments that will rule him out for a couple of weeks and it summed up Everton's early-season injury misfortune when Bent also twisted his ankle.
Bent will also be assessed today, with David Moyes already without Lee Carsley, Gary Naysmith, Per Kroldrup and James Beattie, although Simon Davies could be fully fit by midweek.
"Injuries are part and parcel of football,'' Moyes said. "But we defended very well. It was a constant bombardment and you can count on one hand the teams who will come here this season and win.''
Goal: Bent (52) 0-1.
Bolton Wanderers: (4-3-3): Jaaskelainen; Hunt (Campo, 78), Jaidi, Haim (Vaz Te, 83), Gardner; Okocha, Speed, Nolan; Pedersen (Giannakopoulos, 67), Davies, Diouf. Substitutes not used: Walker (gk), Faye.
Everton: (4-3-3): Martyn; Hibbert, Yobo, Weir, Pistone (Osman, 32); Arteta, Neville, Cahill; Bent (McFadden, 59), Ferguson, Kilbane. Substitutes not used: Wright (gk), Davies, Vaughan.
Referee: A Wiley (Birmingham).
Booked: Everton Kilbane.
Man of the match: Diouf.
Attendance: 25,608.Reuse content