Bolasie’s 63rd-minute strike from outside the area sparked hopes of a fightback for the Toffees who had gone down to three first-half goals, but the league leaders held on to win 3-1.
However, Allardyce hailed the 28-year-old’s selfless display as well as the quality of his first goal of the season.
“He did a good job,” Allardyce told club website.
“Not only with his work-rate but also in looking after one of the best full-backs in the world at the moment in Kyle Walker.
“He’s had to chase him up and down all day and he finally got his reward for that by the way he got the ball and finished. He produced a goal which lifted everybody and we tried to move on from there.”
After having to begin the season late due to his rehabilitation from an injury that has kept him on the sidelines since December 2016, Bolasie has stepped up in recent weeks.
And he will be hoping to continue on the same wavelength as ninth-placed Toffees go head-to-head against in-form archrivals Liverpool in next week's Merseyside Derby.