Chelsea were in control from start to finish against a Swansea side who failed to muster a single shot on target, but they were left to rely on a somewhat scruffy Rudiger effort to claim a win that keeps the gap to second-placed Manchester United at three points.
Conte was given his marching orders towards the end of the first half, when he lost his temper after his side were wrongly denied a corner.
But the Italian will have breathed a sigh of relief when his side eventually and deservedly went in front – Rudiger heading home after N'Golo Kante's effort took a huge deflection off Swansea striker Wilfried Bony.
While Chelsea will be grateful to emerge with the three points, Swansea's concerns in front of goal continue following a fourth successive match without finding the net.
Eden Hazard dropped to the bench in one of four changes to the Chelsea side that drew 1-1 with Liverpool on Saturday and Willian – one of the players to come in following his equalising goal at Anfield – came close to opening the scoring in the 10th minute.
74 - Cesar Azpilicueta isn't starting a Chelsea PL game for the first time since December 2015, having played 90 minutes in each of the Blues' last 74 top-flight matches. Dave. pic.twitter.com/sC3WXW65o2— OptaJoe (@OptaJoe) November 29, 2017
The Brazilian's free-kick from the left curled just around the post after Marcos Alonso came within a whisker of getting his head to the delivery.
On-loan Swansea top scorer Tammy Abraham was ineligible to play against his parent club as Bony once again led the line, but the Ivorian saw little of the ball early on, with Chelsea controlling possession and testing Lukasz Fabianski with efforts from Davide Zappacosta, Pedro and Alvaro Morata – a man who has scored more goals in the Premier League this season (8) than Wednesday's opponents (7).
Alonso unsuccessfully hit the deck in search of a penalty under pressure from Renato Sanches after 25 minutes, before Fabianski was called into action again to tip over a well-struck Morata volley.
The wing-back then headed wide and a Willian cross deflected just beyond the left-hand post off Alfie Mawson, but the home side went in at half-time with nothing to show for their 11 shots on goal, while Conte was banished over his furious reaction to the home side not being awarded a corner following Mawson's lucky escape.
Sanches, who arrived in south Wales from Bayern Munich with much promise, was hooked at the interval after another ineffective outing in the Swansea midfield, and Chelsea finally got their goal 10 minutes into the second half.
Bony got his head in the way of a fierce Kante drive but only managed to divert it into the path of the advancing Rudiger, who used his own head to power the ball beyond Fabianski.
8 - Chelsea have scored more headed goals in the Premier League this season than any other side. Nod.— OptaJoe (@OptaJoe) November 29, 2017
Swansea finally drew a save from Thibaut Courtois when Jordan Ayew fired across the six-yard box from a tight angle, but it was the sum of what the visitors could manage against a Chelsea side who should already have been out of sight.
KEY OPTA STATS
- Cesar Azpilicueta didn’t start a Premier League game for Chelsea for the first time since December 2015, having played 90 minutes in each of their last 74 top-flight matches.
- Chelsea have scored eight headed goals in the Premier League this season; more than any other side.
- Chelsea have remained unbeaten in the Premier League in November (W3 D1 L0) – the first month this season in which they haven’t lost a league match.
- Only three clubs have scored fewer goals after 14 games of a Premier League season than Swansea City (7) this season: Derby (5 in 2007-08), Bradford (5 in 2000-01) and Man City (6 in 1995-96).
- Swansea failed to attempt a single shot on target in this match – the fourth time they haven’t had one in a Premier League game already this season.
- Overall in 2017-18, the Swans have attempted a league-low 24 shots on target in the Premier League.