Chelsea weren’t troubled by their manager’s absence from the bench and clinched the points early in the second half when Germany defender Antonio Rudiger headed his first league goal since his pre-season move from Roma.
Despite recording a fifth win in their last six league games, third placed Chelsea remain well behind leaders Manchester City and it will take a major surge for the champions to successfully defend the title.
With a host of matches against teams outside the top half of the table coming up in December, they will hope to at least close the gap on City heading into the new year.
Swansea stay second bottom as the pressure mounts on boss Paul Clement, whose team are without a win in six league games and haven’t scored in their last four.
It was far from a vintage display from Chelsea, with Conte’s decision to rest Eden Hazard after his fine performance in Saturday’s draw at Liverpool depriving the Blues of their creative catalyst.
Hazard wasn’t the only one given a breather by Conte as defender Cesar Azpilicueta was out of the Chelsea starting line-up in a league game for the first time since December 2015.
After a sluggish start on a freezing evening, Chelsea should have had a penalty when Alvaro Morata was grabbed by the neck and wrestled to the turf by Swansea defender Mike van der Hoorn.
Despite Morata’s complaints, Swarbrick waved play on, but Chelsea were back on the attack moments later as Willian whipped an inswinging free-kick just wide.
Conte this week warned the players he has used sparingly this season not to grumble about their lack of opportunities.
Pedro, among those played less frequently by Conte, wasted a chance to catch the eye when he shot too close to Swansea goalkeeper Lukasz Fabianski from a good position.
Swansea were utterly toothless without Tammy Abraham, the young striker on loan from Chelsea who had scored four times this season but wasn’t allowed to play against his parent club.
Chelsea went close again when Cesc Fabregas chipped a pass towards Morata, who was facing away from goal but quickly shifted his body for an agile volley that Fabianski tipped over.
When Willian drilled in a low cross that Swansea defender Alfie Mawson nearly deflected into his own net, it seemed only a matter of time before Chelsea took the lead.
But Swarbrick awarded a goal-kick instead of a corner for that incident and Conte responded with his angry tirade at Mason.
Sent off by Swarbrick, Conte retreated to the seats behind the Chelsea bench, where he continued to shout towards Mason before eventually calming down.
If Conte had struggled to keep his blood pressure down in the first half, the Italian must have been cursing again soon after the interval when Pedro wastefully blazed over from Willian’s cross.
But Conte’s mood was finally lifted as Rudiger broke the deadlock in the 55th minute.
N’Golo Kante’s shot from the edge of the area took a wicked deflection off Swansea’s Wilfried Bony and Rudiger reacted smartly to head home from close-range.
Morata almost finished off Swansea with a towering header that forced an excellent save from Fabianski, but despite their lack of killer instinct Chelsea had done enough.
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