Bournemouth led after 17 minutes after the Spanish U21 international's header from a corner, the 19-year-old netting his first for the club.
The hosts had a number of opportunities to add to their lead in the second half as Spurs pushed for an equaliser, but they weren’t able to find it and the Cherries secured the points.
Andoni Iraola made two changes to his starting 11 that beat Wolves last weekend.
Huijsen and Antoine Semenyo came into the side, in place of Marcos Senesi and David Brooks, with the former dropping out of the squad through injury, while the latter dropped to the bench.
For Spurs, Ange Postecoglou named former Cherries striker Dominic Solanke in his starting side to face his old club for the first time since joining Spurs in the summer.
The visitors got the game underway, with defender Ben Davies booked in the early exchanges as the Cherries looked to break through Evanilson.
It was Spurs who had the first chance of the game, Dejan Kulusevski shooting straight at Kepa after good work by James Maddison in midfield.
Solanke shot over after eight minutes, before Evanilson had the Cherries first shot on target from very close range, Fraser Forster diverting behind.
And from the resulting corner, the hosts opened the scoring.
Huijsen peeled round to the back post and was unmarked to put a fantastic header past the Spurs keeper.
Yves Bissouma went into the book for a foul on Justin Kluivert, before Marcus Tavernier had the ball in the back of the Spurs net, but the flag was up for offside.
The Cherries went close to doubling their lead just before the break, as a Tavernier header from a Kerkez cross was well saved by Forster down to his left, as the Cherries headed into the interval with their one goal lead intact.
Bournemouth had the best early chance in the second period, Kluivert’s shot saved by Forster after a brilliant break by the Dutchman, after Kepa had done well to punch off the line from a Spurs corner moments before.
Spurs went close but a Kulusevski cross was just too high for the arriving Davies, before Son Heung-Min had the ball in the back of net in his first action since replacing Pape Matar Sarr, but he was offside.
Evanilson saw a shot saved by Forster, before Maddison curled an effort just past the post.
Iraola went to his bench, Dango Ouattara replacing Kluivert, before Kepa saved well from Pedro Porro’s first time volley after the keeper punched clear a corner.
Christie hit the post for the home side minutes later, after good link up play between he and Evanilson, the Scot’s effort just going wide off the woodwork.
The Brazilian had the ball in the back of the net with just under 20 minutes to play, but this too was offside.
Tavernier curled a shot wide after good work in the press from Evanilson, before Ouattara blasted wide after good work from Adams in midfield to win the ball back.
Lewis Cook replaced Christie, before Tavernier fired a good chance over the bar after Semenyo’s cut back as the game entered the final ten minutes.
Ouattara fired over a good Cherries chance, as Iraola made a triple change for the final five minutes, Enes Unal, Philip Billing and David Brooks replacing Evanilson, Tavernier and Semenyo.
Unal had a good chance shortly after but fired straight at Forster, before Ouattara again fired high and wide after a Cherries counterattack.
The Cherries held off Spurs in six added minutes as they took the points to move into the top ten of the Premier League and above their visitors.
AFC Bournemouth: 13, Kepa (booked, 62'); 3, M. Kerkez; 2, Dean Huijsen; 27, I. Zabarnyi; 15, A. Smith (c); 10, R. Christie (L. Cook 77'); 12, T. Adams (booked, 68'); 16, M. Tavernier (P. Billing 85'); 19, J. Kluivert (D. Ouattara 64'); 24, A. Semenyo (D. Brooks 85'); 9, Evanilson (E. Ünal 85').