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 Australian Ange Postecoglou's disappointing Spurs team that failed to take advantage of the growing discontent surrounding the home side.
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.
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.
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