Demba Ba's 28th-minute goal saw Chelsea return above Tottenham to third place in the Barclays Premier League for 24 hours at least, ahead of Saturday's north London derby.
West Brom had not won a league match at Chelsea in almost 35 years, and although owner Roman Abramovich may be content with Benitez in charge until the end of the season and a fifth win in seven games, that may not be enough to appease Blues fans.
There is recent precedent for a change of Chelsea manager following losses to West Brom, with the Baggies the final Premier League opponents for both Andre Villas-Boas and Roberto Di Matteo.
Many wondered if this would be Benitez's last stand following his rant against the title of 'interim manager' and the fans' incessant barracking of him.
Much of the focus was on the Spaniard after his midweek deviation from measured politician to rabble-rouser.
Due to his prior association with Liverpool, Benitez's temporary appointment was never a popular one, but he hoped the crowd would use their energies to back the team.
They came with handmade banners - "The Interim One" and "Rafa Benitez we're just not that inter im" among them - and would have been unhappy to see captain John Terry named among the substitutes, alongside Fernando Torres, as one of seven changes to the side which progressed in the FA Cup at Middlesbrough.
Benitez says he will decide whether Terry, with his fitness travails, can play twice a week and the defender's armband was passed to Frank Lampard, who moved equal with John Hollins as the club's third-highest appearance maker on 592.
Benitez quietly took his seat - it took a few moments for his arrival to be greeted with the usual expletive-laden chants - and Chelsea almost went ahead in the fourth minute.
Ba crossed from the right for Oscar, but Ben Foster, who has made himself available again for England, saved instinctively in front of the watching national manager Roy Hodgson.
Juan Mata, on his 100th Chelsea appearance, volleyed wide across goal before Steven Reid's long-range effort was tipped over by Petr Cech.
Oscar should have had a rare headed goal when he met Mata's clipped cross to the back post after 16 minutes but could not convert.
Following the move, the Stamford Bridge patrons observed their homage to Di Matteo, but there was also plenty of encouragement for the players on the pitch, so perhaps Benitez's midweek comments that the fans should put their effort into supporting the team had been heeded to some extent.
Ba shot straight at Foster after latching on to a loose ball and Oscar screwed another effort over.
Eden Hazard almost took advantage of indecision in the Baggies defence before Claudio Yacob's foul on Oscar presented Chelsea with a free-kick opportunity.
David Luiz's effort ricocheted off the wall and Foster scrambled it out for a corner, from which Chelsea went in front.
The left-sided set-piece was played short to Oscar, whose inswinging cross towards the back post found Luiz and occupied the attentions of Foster.
Luiz headed the ball back across goal for Ba to sweep it in.
Mata shot wide soon after before Oscar, twice, and Cesar Azpilicueta had efforts blocked.
Lampard, seeking his 200th Chelsea goal, had an effort ruled out early in the second half, with Mata flagged offside in the build-up.
After 60 minutes, Benitez and the Blues fans reacted in unison in appeal for a penalty.
Oscar's lofted ball forward was brought down by Hazard, who went down under pressure from Jonas Olsson, but referee Kevin Friend was unmoved.
There were more boos at the Bridge when Peter Odemwingie finally got his wish to play in west London - albeit not at QPR - and came on as a substitute.
The single-goal advantage was not a comfortable one for Chelsea and Benitez was animated in his technical area, even rising to his feet as the fans chanted "Stand up if you hate Rafa".
Chelsea again threatened and again Foster saved from Oscar.
Azpilicueta's cross was headed down by Ba for the Brazilian, who scuffed his shot straight at the goalkeeper.
Oscar again saw an effort saved by Foster before Cech had to tip over a dipping Odemwingie free-kick.
Cech was called upon from the resulting corner as the ball was directed goalwards off the head of his team-mate Azpilicueta.
A Victor Moses cross was just behind his fellow substitute Torres and Odemwingie had an effort saved by Cech.
Foster came up for a stoppage-time corner, but the hosts held on for three points to the relief of Benitez.