The Blues interim manager angered the supporters with his midweek comments, and was greeted with boos upon his appearance at Stamford Bridge.
However, his Chelsea side soon quieted the crowd with a stylish first-half display, which was capped off by Demba Ba's strike.
That proved to be the only goal of the game as the European champions held off a late Baggies rally to claim a victory which sees them climb above Tottenham Hotspur to third in the Premier League table.
Below, you can read how the action unfolded in West London.
2.11pmAfternoon all! Benitez may be under pressure to please the Chelsea fans, but he has resisted the temptation to recall Blues favourite John Terry this afternoon.
2.14pmThe Chelsea skipper has found himself on the bench for Premier League duties since returning from injury last month.
2.23pmDemba Ba, who won't be wearing a face mask to protect his now-unbroken nose, is preferred to the misfiring Spaniard up front, and will be supported by the attacking midfield trio who brought Di Matteo success at the start of the season.
2.25pmJuan Mata, Eden Hazard and Oscar, recalled in place of John Obi Mikel, will be charged with creating chances for Ba, who has not netted in his last seven appearances.
2.28pmIn another tactical alteration, Ramires takes up his favoured central role and will play alongside captain for the day, Frank Lampard, who is just one strike away from 200 Chelsea goals.
2.30pmOne Chelsea player who will not be featuring this afternoon is Romelu Lukaku.
2.32pmThe Belgian is ineligible as part of the agreement which took him to West Brom on loan from their Stamford Bridge opponents.
2.34pmLukaku has scored 12 Baggies goals this season, including a double in their victory over Sunderland last weekend.
2.36pmHis absence will come as a blow to Clarke, but is cushioned by the fact that Shane Long has shaken off a knock to start as the lone striker.
2.38pmAfter opting for 4-4-2 last week, Clarke has switched to a 4-2-3-1 system this afternoon to match Chelsea's predicted formation.
2.39pmMarc-Antoine Fortune and Graham Dorrans come into the lineup, with Chris Brunt missing out. Jonas Olsson takes the captain's armband in Brunt's absence.
2.41pmPeter Odemwingie, who attempted to force through a transfer deadline day move to QPR, is again named on the West Brom bench after reconciling with manager Clarke.
2.42pmSixteen-year-old Isiah Brown is also among the Baggies substitutes and will become the youngest player in Premier League history should he come on.
2.45pmMatthew Briggs, at 16 years and 65 days old, is the current holder of the record, but Brown is 11 days younger than the Fulham man was when he made his top-flight bow in 2007.
2.48pmIn West London, we have plenty of signs of the Rafa revolt. The Spaniard pleaded with the Chelsea fans for unity but there is a number of banners and signs displaying their continued displeasure at his tenure.
2.50pm'Divided we fall. #Rafaout.' 'Rafa Benitez - we were never inter 'im'. And the simple, 'Rafa out' are among the words of protest.
2.52pmUnder 10 minutes until kickoff now, will the anti-Benitez atmosphere at the ground have a negative influence on Chelsea's performance? Rafa certainly thought they had based on his midweek press conference.
2.55pm"I'm disappointed with some fans. They have to support the team instead of wasting time making banners," he told reporters.
"They have to support the team. They gave me the title of interim manager which is a massive mistake. I am the manager and I will manage this club. The fans are not helping us.
"I am a professional and I will do my job. At the end of the season I will leave."
2.57pmPREDICTION: Despite Chelsea fans' vocal unacceptance of Benitez, I think the absence of powerhouse Lukaku will limit West Brom's attacking threat and I expect the Blues to triumph 2-0.
0 minWe are underway at Stamford Bridge, where West Brom have never won in six Premier League visits...
2 minBoos greet Benitez as he strolls out to the edge of his technical area for the first time. How unsurprising.
3 minSAVE! Ba fizzes a low cross into the box and Oscar, who had run inbetween the two West Brom centre-backs, hits a side-footed shot from eight yards which is palmed away by Foster. Great chance, good save.
4 minSHOT! Oscar is involved again, delightfully flicking a lofted Ramires pass towards Mata, who volleys first time across Foster's goal and a few yards wide.
6 minSHOT! Steven Reid strikes a powerful free-kick from distance and forces Cech to turn the ball around the post. The resulting corner comes to nothing.
8 minIn the circumstances, a bright start from Chelsea, who hand a 100th club start to Juan Mata and 200th Premier League appearance to Ashley Cole. Landmarks.
10 minChelsea keep possession comfortably in midfield, but with every West Brom player apart from Long behind the ball, they cannot break them down on this occasion.
11 minThat is suggestive of how Clarke has approached this game - defend with 10 players and then hope to hit the hosts on the counter. Those tactics worked in the 2-0 win over Liverpool earlier this month.
13 minTo find any cracks in the defensive West Brom lineup, Mata, Hazard and Oscar will have to be at their creative best, but the trio have been starved of the ball in the last five minutes.
15 minCHANCE! Right on cue, two of them combine to set up another great chance for Oscar. Mata cuts in from the right and flights a cross in towards the Brazilian, who heads unmarked straight into Foster's gloves.
16 minThe 16th minute on the Stamford Bridge clock is greeted with the usual chants celebrating their Champions League winning manager Roberto Di Matteo, who wore the number 16 shirt during his Chelsea playing days. The Italian was axed earlier this season and replaced by Benitez, who, needless to say, is not thought of so fondly.
18 minSHOT! A West Brom clearance falls kindly to Ba, who runs along the edge of the box before shooting low. He connects well with his weaker left foot, but, again, the effort is directly at Foster.
21 minBa flicks an Ivanovic punt into the path of Mata, whose first touch is poor. Oscar is on hand to retrieve the ball, though, and strikes over the crossbar from 25 yards.
23 minThe 21-year-old has yet to find the net from open play in the Premier League. His sole English top-flight goal came from the penalty spot in the 8-0 thrashing of Aston Villa. He has scored eight times in other competitions this season, though.
24 minHere, the Brazilian turns cleverly on the left to get away from Reid and then delivers a cross which is just too high for Ba.
25 minWest Brom have not been victorious at Stamford Bridge in 34 years, and have never beaten or scored against a Rafael Benitez team in the Premier League. Not good omens, but they have held out for the opening 25 minutes today.
28 minAfter Foster saves well from a Luiz free kick, Chelsea take the resulting corner short. Oscar stands a cross up to the back post, which Luiz heads across goal for Ba to simply poke home from six yards. A deserved lead for the Blues.
30 minSHOT! Mata picks the ball up in the centre of the goal, an area where he can be so dangerous. He attempts to slide in Ba and when the pass rebounds straight back to him, the Spaniard volleys a couple of yards wide of the left post.
32 minOn the week when he announced his availability for England selection once again, Foster kept Chelsea at bay with some fine early saves, but could do nothing about Ba's opener. It was sloppy defending at the back stick by Gareth McAuley and Luiz's headed cutback was easy pickings for the Chelsea striker.
33 minFortune skips past Cole down the West Brom right, but has no Baggies teammates to aim for in the box. The visitors need to attack with more bodies when they counter.
37 minSHOT! Mata drifts a corner over the crowd of players and Oscar meets it with a first-time volley which is deflected behind for Chelsea's seventh corner of the half.
39 minBLOCK! Lovely play from Chelsea as Mata, Ba and Oscar link up intricately to set up a shooting chance for the Brazilian. Olsson throws himself in front of the strike and then blocks again from Azpilicueta's follow-up.
41 minA superb 40-yard crossfield pass from Ramires puts Mata through on goal, but the Spaniard is adjudged to be offside.
42 minMorrison latches onto a Fortune knockdown and slices an ambitious 25-yard volley high into the stands.
43 minIvanovic charges out from the back and releases Hazard down the left. The Belgian drifts inside unchallenged but his bending effort intended for the bottom corner is thwarted by Reid's outstretched foot.
45 minWe are entering first-half stoppage time, of which there will be one minute...
3.51pmNo signs of the boos that greeted Benitez at kickoff as Chelsea leave the pitch for the break. The Blues have been excellent and completely dominant during the opening 45 minutes and are fully deserving of their 1-0 lead, which came courtesy of Demba Ba.
3.53pmThe Senegalese striker netted his first goal in seven matches by converting David Luiz's headed cutback from eight yards. It has been Mata and Oscar who have been central to Chelsea's success, though.
45 minMata tries his luck early on with a dipping 30 yard volley which drifts harmlessly wide of Foster's goal.
47 minHazard shows some tricky feet on the left edge of the area before pulling the ball back for Lampard, whose drive is blocked by McAuley.
49 minDISALLOWED! Lampard has the ball in the net but is denied his 200th Chelsea goal by the assistant referee. Hazard drifts inside and may have played in the England midfielder earlier, but instead chips towards Mata, who is several yards offside when he squares for Lampard to tap in.
51 minClaudio Yacob's foul on Ramires presents Lampard with another opportunity, but he blasts the free kick straight against the wall.
54 minCHANCE! Oscar's cross splits the West Brom defence wide open but is behind Ba, who attempts to flick it goalwards. He doesn't make great contact and is fortunate to get a second opportunity, which is blocked by the legs of Foster.
56 minBOOKING! The first yellow card of the afternoon is brandished by Kevin Friend, with Hazard cautioned for a trip on Fortune.
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58 minWest Brom have not committed enough numbers forward to threaten an equaliser, or even keep the ball when they have had rare ventures into the Chelsea half.
60 minPENALTY SHOUT! Olsson shrugs Hazard off the ball and the Belgian falls to the floor, optimistically appealing for a spot kick, which is not forthcoming.
62 minSUBSTITUTION: On the day Chelsea boss Benitez was greeted with boos, West Brom's own villain Peter Odemwingie is brought on to replace Marc-Antoine Fortune to a warmer ovation. It seems all is forgiven then, as the last time Odemwingie was in London he was trying to force through a move to QPR.
64 minBOOKING! Hazard is too tricky and too pacey for McAuley, who sythes down the Belgian near the left byline, just outside of the area.
66 minBenitez's movement to the edge of his technical area is again greeted by boos and simultaneous chants calling for the reappointment of Jose Mourinho. The former Chelsea manager is odds-on favourite to return to Stamford Bridge at the end of the season.
68 minOdemwingie's introduction presents the Baggies with another body up-front, and another goal threat. While Chelsea have been dominant, their advantage is only a slender one and as we know in the Premier league, anything can happen.
70 minSUBSTITUTION: Clarke makes a second attacking change, replacing Dorrans with Jerome Thomas, who chalks up 100 Baggies appearances in the process.
73 minLuiz is forced to concede a corner as McAuley attacks a Morrison free kick at the back post. Chelsea deal with the set piece comfortably, though.
75 minSAVE! Azpilicueta launches a ball forward, which is headed down by Ba. Oscar picks up the loose ball and shoots but Foster gets down well to gather the strike.
78 minSUBSTITUTION: Victor Moses, excellent in the FA Cup victory over Middlesbrough in midweek, comes on for the final 12 minutes in place of Eden Hazard.
80 minSAVE! Foster denies Oscar for the fourth time this afternoon. This is probably the pick of his saves, as Oscar superbly wriggles away from Yacob and then fools the visiting defenders by feinting to shoot. He eventually gets a strike away which has Foster at full stretch to fingertip the ball clear.
82 minSUBSTITUTION: Clarke makes his final alteration, chucking on another striker in the shape of Markus Rosenburg and sacrificing holding-midfielder Yacob.
83 minSAVE! At the other end, Cech produces an equally good stop to foil Odemwingie. The Nigerian's dipping 30-yard free kick looks to be sneaking under the crossbar before the Blues keeper tips it over.
84 minSAVE! Azpilicueta inadvertantly diverts the resulting corner towards his own goal but Cech is on hand to claw the ball away. He's been almost redundant all day, but the long-server home stopper has done his job when called upon in the final stages here.
86 minChelsea counter through Moses, who has options to his right but instead selfishly goes on his own and blazes the shot off target.
88 minSUBSTITUTION: Potential match-winner Demba Ba makes way for Fernando Torres.
90 minWe are entering stoppage time, of which there will be four minutes. There is still a chance for the Baggies to grab an unlikely equaliser!
90+2 minSHOT! Morrison picks out Odemwingie on the right edge of the box. He cuts inside and shoots low, but Cech is equal to the effort at his near post.
90+3 minSUBSTITUTION: The excellent Mata leisurely leaves the field as Mikel comes on to waste some precious time.
90+4 minWest Brom have a corner, and Foster makes his way forward. He challenges for the initial ball, which is only cleared to Odemwingie. He turns it back into the danger area and Foster remarkably attempts an overhead kick. The Baggies stopper fails to make contact and Chelsea players take a relieved breath as Olsson spoons the ball over the crossbar.
4.57pmThey had to endure a few nervous moments near the end, but Chelsea hang on to claim a well-deserved three points, which see them climb above London rivals Spurs into third.
5.02pmBenitez was expectantly greeted with boos from the Stamford Bridge faithful following his midweek comments, but the negative atmosphere was soon unapparent as Chelsea produced an excellent, crowd-pleasing first 70 minutes. Ba gave them the lead and, although they should have added to his strike, the forward's first goal in seven matches was enough for them to beat an under-par West Brom.
5.05pmThat is it from me for today. Be sure to check back in with Sports Mole for further analysis of Chelsea's win and live coverage of Wigan Athletic vs. Liverpool, which you can follow here. Thanks for joining us this afternoon! Over and out...