A 32nd-minute header from Kevin Davies gave the visitors the lead in a dire and bad-tempered first period, before a disallowed effort from James McFadden sparked Bolton into life.
Stelios Giannakopoulos added a second before a Gary Speed penalty and a glorious drive from the Greece international completed the rout.
Bolton started with typical roughness and had Kevin Davies booked after just 34 seconds for a wild lunge on Phil Neville, while Kevin Nolan was fortunate to escape a yellow card a minute later.
It was a scrappy opening. An array of long balls, misplaced passes and niggly fouls stunted any sense of continuity during the first half hour.
Tempers flared in the stands and on the pitch when McFadden and Jussi Jaaskelainen clashed, and the Bolton keeper theatrically fell to the floor.
Abdoulaye Faye was then booked for trying to punch the ball into the net as the Everton fans and bench continued to rage about the visitors' confrontational approach.
Tim Cahill squandered a promising opening for the hosts when his control let him down in the 29th minute and Bolton capitalised just three minutes later.
Kevin Davies found space in the area and looped in a header which went in off the post, crossing the line despite James Beattie's desperate attempt to hack clear.
No-one looked likely to add to the score before the break, and the start of the second period did little to warm the supporters either.
Kevin Davies cleverly set-up Stelios for the first chance 12 minutes into the second-half, but the Greek's half-volley was easily saved by Richard Wright.
With half-an-hour to go the visitors looked ready to shut up shop and dropped deep into their own half, allowing Everton possession they would have struggled to achieve on their own merits.
The Toffees pinged in cross after cross, but none of sufficient quality to create a clear chance.
Bolton needed the officials to intervene 18 minutes from time when McFadden poked home a long free-kick, but was correctly adjudged to be offside.
What followed was a massacre, which not a single person in attendance had envisaged.
Substitute Ricardo Vaz Te strolled through the home defence and laid the ball off to Stelios, who drilled it past Wright on the angle on 75 minutes.
Nuno Valente then needlessly mauled Kevin Davies in the area, allowing Speed to score a penalty against his former club, three minutes later.
Stelios completed the rout in the 80th minute with an unerring strike into the top corner to give Wanderers a third straight away win.
Everton had their best chances then through Leon Osman, Beattie and Mikel Arteta, but the only Christmas carol echoing around Goodison was the deafening chorus of boos which serenaded them from the field.
For Everton there are still relegation worries to occupy their festive season. Bolton, already progressing well in the UEFA Cup, are back on the European trail.