The former Standard Liege man had grabbed a second-half equaliser against Manchester United four days earlier.
And the midfielder was once again the Toffees hero as he headed home Steven Pienaar's cross via a post to seal David Moyes' side first win in six games.
The defeat piles the pressure on Bolton boss Gary Megson, booed by his own fans at Tottenham at the weekend, with Wanderers having won just once in their last ten games and scoring only a single goal at home in four attempts.
Bolton had not won at the Reebok since the opening-day victory against Stoke City but they started brightly with Riga Mustapha, making his first start in the Premier League in Megson's new-look 4-4-2 formation, forcing Tim Howard into a save low down to his left from 25 yards on four minutes.
Louis Saha thought he had put Everton in front on 11 minutes when he put the ball in the net but the referee's whistle had already gone for an infringement by Yakubu.
Jussi Jaaskelainen then fumbled Saha's low drive but the Wanderers goalkeeper gathered at the second attempt. Moments later Fellaini headed over from Phil Jagielka's deep cross.
But it was the home side, who had not scored in three of their last four games, who finished the half the stronger.
First defender Gary Cahill just failed to make contact with Riga's dangerous corner before, three minutes before half-time, Matty Taylor headed just wide of the upright after Kevin Davies had flicked on Gretar Steinsson's long throw.
Both sides struggled to carve out chances - or even find anything close to warming the cockles on a bitterly cold evening - in a second half littered by fouls which disrupted what little flow to the proceedings there was.
Moyes brought on Tim Cahill, back from a three-match suspension following his red card in the derby defeat against Liverpool, for the ineffectual Yakubu, but even the Australian struggled to make an impact.
Taylor, who scored Bolton's last goal in their 3-1 victory at West Ham three games ago, went closest to breaking the tedium but the midfielder could not turn in Steinsson's low cross at the near post on 69 minutes.
Instead it was left to Fellaini to break the deadlock and pile on the misery for Megson as the boos rang out around the Reebok from the Bolton fans at the final whistle.