Enzo Maresca's side were under pressure after limping into the international break playing football that had ceased to excite home fans.
But they largely had the better of a disappointing Spurs team in a game that left Australian boss Ange Postecoglou frustrated after a lengthy review denied Tottenham an equaliser.
As when these teams met in north London last season, VAR played a prominent role, ruling out goals from Moises Caicedo and Pape Sarr after half-time, but Chelsea deserved the points.
In Postecoglou's view the technology was "killing the game".
"It's not the same game it used to be. You just don't know what you're going to get and you're standing around for 12 minutes," he said.
"It's killing the game but no one cares about that. I think everyone loves the drama, the controversy.
"If the referee saw that and then he needs to see it for six minutes, tell me what's clear and obvious about it mate?"
Spurs had themselves to blame for Chelsea's opener five minutes into the second half.
After Sancho had been given freedom inside the box to pirouette on the ball, assess options and lay it off, Udogie did little but stand and watch as Fernandez drifted across him to meet Palmer's cross and nod his side in front with the simplest header.
Caicedo then thumped the ball into the bottom corner only to be denied after a hugely protracted VAR check that judged Colwill to have strayed offside by an almost imperceptible margin.
Spurs were then themselves denied by a pitchside review after Sarr had lashed in what looked a stunning equaliser from long range, the Tottenham substitute having caught Caicedo on the knee in winning the ball for which he was shown a yellow card.
Sanchez kept out Son for a second time after a Spurs counter in the final minute of the 90, before 12 additional minutes during which Postecoglou's side failed to put Chelsea under much pressure to challenge their lead.
With three losses in the past five games, Tottenham remain in 14th place in the league but still comfortably clear of the relegation zone.