Leandro Trossard finished off a lovely team move to give Brighton a first-half lead with the game's only goal, firing past Hugo Lloris from a Pascal Gross cut-back after the hosts split open Spurs' back line.
Brighton continued to have the better of the chances in the opening portion of the second half, with Spurs keeper Lloris saving from a Ben White shot before Neal Maupay headed wide of the target shortly after.
There were nervy moments for Brighton down the stretch, but the home side held firm to see out the result and take a crucial three points to put further distance between themselves and the relegation zone.
Jose Mourinho's Spurs remain in sixth place on 33 points from 20 matches so far this campaign.
"It's our best performance this season and last. From start to finish we did what we needed to do, created some chances, scored a really good goal, good attitude around the pitch, good quality, against a top opponent," Brighton manager Graham Potter said.
"I thought it was closer to a 2-0 than a 1-0. I am really proud of the players."
Out-of-form Tottenham's second defeat of the week after Thursday's 3-1 home loss to Liverpool leaves them in sixth place, six points off the top four having won only two of their last nine league games since topping the table.
"In the first half I felt the team was probably too sad with the goal conceded and the situation," Mourinho said. "There was a lack of energy. In the last 25, 30
Brighton have taken seven points from their last nine and thoroughly deserved their first home league win since June.
They could have taken the lead even earlier as Gross clipped the post after a neat build-up.
Tottenham did not learn their lesson though and Brighton's slick approach play caused them no end of problems.
It was a similar move that led to the goal with Alexis Mac Allister playing in Gross who reached the byline before picking out Trossard to finish with ease.
Vinicius forced a fine save from Sanchez and Son Heung-Min had a couple of shots at goal, but it was Brighton who went closest to scoring again as Aaron Connelly's finish from point blank range was somehow kept out by Toby Alderweireld.
Brighton's joy was clear at the final whistle as they finally found some home comfort.
"It's a confidence boost, we have worked hard all season, now we have won at home and we have a taste for more," match-winner Trossard said.