The England forward struck from the spot after Max Kilamn was adjuged to have blocked Bernardo Silva's cross with his arm.
Wolves set up with five at the back and sought to frustrate City and, for much of the opening 45 minutes, they succeeded.
They were disciplined and defended in numbers, limiting the space in which City could create.
But a first half light on clear-cut chances for ether side suddenly sparked into life when Raul Jimenez was sent off in stoppage time at the end of the first period after being booked twice in the space of 31 seconds, his second for stopping Rodri’s free-kick being taken.
It was a moment of madness that left the visitors with an uphill task.
And there was time for more drama before the break when Jack Grealish felt his cross was blocked by the arm of Max Kilman, but John Moss waved away the penalty claims.
A City goal felt likely and the breakthrough came from the spot. Joao Moutinho blocked Bernardo Silva's cross with his arm and, after a lengthy VAR check, a penalty was given.
Raheem Sterling converted calmly to score his 100th Premier League goal.
Grealish should have made it 2-0 moments later, but his effort from close range was off target, and Bernardo's powerful drive was saved superbly by the legs of Sa.
It was a tense finale, but City were deserved winners.
100 - Raheem Sterling has scored his 100th goal in the Premier League. Sterling is the 32nd player to reach this total in the competition, and the eighth-youngest at 27 years and 3 days. Centurion. pic.twitter.com/QGKaeoPwwR— OptaJoe (@OptaJoe) December 11, 2021
Raheem Sterling became only the 32nd player to enter the Premier League 100 club with his opener in this game.
And at 27 years and three days, he is the eighth youngest player to reach the milestone.
It's the latest statistic underlining his continued excellence.
Sterling joined City in the summer of 2015 and has since gone on to win three Premier League titles, one FA Cup and five league Cups.
He is also a star on the international stage. He was named in the Euro 2020 Team of the Tournament after leading England to their first major final for 55 years in the summer.
He has now played 72 times for England, scoring 18 goals.
Ederson was rarely called upon during this match, but with seconds remaining he tipped over Max Kilman's header to preserve his clean sheet.
And it was his 100th shutout for City in just 212 games!
32 - @ManCity have won 32 of their 40 Premier League games in 2021 (D2 L6) – only Liverpool in 1982 (33) have won more matches in a single calendar year in English top-flight history. Unwavering. pic.twitter.com/su4rt1sja2— OptaJoe (@OptaJoe) December 11, 2021
Tight at the top
Wolves were incredibly well organised and threatened to frustrate City - but we found a way to win.
This may not have been vintage City, with our free-flowing football stifled by Wolves' resolute defending, but it represents three vital points just days after a European away match.
With Liverpool and Chelsea in touching distance just behind us in the Premier League table, it's going to be one of the tightest title races in recent memory.
Strap and in and get ready for some nerve-racking days ahead.
"It's a great number at his age, 100 goals is a lot.
"Congratulations. Like the100 clean sheets from Eddie - congratulations to both and to the team, of course."
(On the game)
"In general we were good. We were not so clever in the final third, some players dropped their performance and some players are coming into their best.
"We conceded one chance in 94 minutes. We created chances to score more but we were not clinical enough to convert them."
Wolves XI: Sa, Samedo, Kilman, Coady, Saiss, Ait-Nouri, Neves, Dendoncker, Moutinho, Jimenez, Traore (Hwang 67')
Subs: Ruddy, Hoever, Marcal, Podence, Trincao, Boly, Silva, Hwang, Cundle
What it means
City’s lead at the top of the Premier League table is extended to four points, for the time being at least.
Liverpool, who sit second, face Aston Villa at Anfield at 15:00 (UK) today and can close the gap back to a singe point with a win.
Third-placed Chelsea, a point further back, also kick off at 15:00 (UK) as they host Leeds United.
It seems clear this season’s title race will be keenly-contested, with all three sides looking like worthy champions. December and January, with domestic fixtures aplenty, looks like being a key period.
The fixtures come at a rapid rate in December. Our next assignment a Premier League home game against Leeds United on Tuesday, which sparks a breathless run of five games in 19 days.
That one kicks off at 20:00 and we will have full coverage on ManCity.com and the official Man City app.
We then travel to Newcastle United on Sunday 19 December. That one is a 14:15 kick off.
News about Man City v Wolves
Pep pleased with Sterling courage
Pep Guardiola says he is grateful Raheem Sterling had the nerve to step up and take the penalty that proved to be the only goal of the game against Wolves. Watch more.
Sterling joins Premier League 100 club with goal v Wolves
Raheem Sterling has scored 100 Premier League goals after his penalty opened the scoring against Wolves. Read more.
City 1-0 Wolves: Extended highlights
City maintained top spot in the Premier League with a hard-fought win over Wolves on what proved a landmark day for both Raheem Sterling and Ederson. Watch more.
Sterling joins Premier League 100 Club | City 1-0 Wolves
Wolves made things hard for City but Raheem Sterling's 100th Premier League goal sealed a narrow - but vitally important - victory. Watch more.
CITY+ Pitcam highlights: City 1-0 Wolves
Raheem Sterling's 100th Premier League goal was enough to earn City a hard-fought 1-0 win over Wolves. Watch more.
Full Match Replay: City v Wolves
Our full game replay, from the first minute to the last... Watch more.
City 1-0 Wolves: Brief highlights
It was a day of twin memorable milestones as City make it six Premier League wins on the bounce at home to Wolves... Watch more.
The impressive numbers behind Raheem Sterling’s Premier League century
Raheem Sterling reached another significant career milestone when he netted his 100th Premier League goal in Saturday’s 1-0 win over Wolves. Read more.
Ederson clocks up a century of City clean sheets
Ederson has now kept 100 clean sheets for Manchester City after his latest shutout against Wolves. Read more.
Amazing stats behind Ederson’s century of clean sheets
Ederson’s achievement in amassing a century of clean sheets for Manchester City is just the latest evidence of his pivotal role in the Club’s success since he joined us from Benfica in 2017. Read more.
Guardiola hails City centurions Ederson and Sterling
Pep Guardiola paid tribute to century makers Raheem Sterling and Ederson after the pair’s latest crucial contributions helped City overcome 10-man Wolves 1-0 at the Etihad to stay top of the Premier League table. Read more.