The Premier League strugglers came from a goal down with a fortuitous leveller just before the break and held firm after the break despite constant City pressure.
Albion keeper Sam Johnstone made two point-blank saves in added time to preserve the visitors' point.
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City were lucky not to fall behind after just eight minutes after a deflected cross fell kindly to Karlan Grant and the West Brom striker shimmied inside before firing a low shot at goal that Ederson did well to push out.
Then, as so often happens at the Etihad, it was a case of ‘break us down if you can’ from the visitors, who defended in numbers, pressed high and were committed to their game plan.
Remaining patient is something City have learned to do over the years, knowing that opportunities will eventually come – and on the half-hour, finally, one did.
Joao Cancelo spotted Raheem Sterling’s run on the right of the box, played the ball though and Sterling’s check back and pinpoint pass back into the middle was swept home powerfully by Ilkay Gundogan to finally break the deadlock.
Just before the break, the visitors levelled with a goal that had more than a touch of good fortune about it.
A free-kick was only half-cleared and as the ball was headed back towards the box, Semi Ajayi took a swing and Ruben Dias deflected a shot that was going well wide past Ederson.
Whether it was deserved or not mattered not a jot – West Brom had ended our run of six consecutive clean sheets, were level and City had work to do again after half-time.
City began the second period by noticeably moving the ball quicker.
The first-half pace had been measured and steady and Pep Guardiola clearly wanted more urgency.
But City were struggling to break down the massed ranks of red and yellow striped shirts.
Kevin De Bruyne, working tirelessly to fashion a goal, came close to beating Sam Johnstone on his near post in the 68th minute, but the Albion keeper kept the shot out with his trailing leg.
But as the game wore on, so City’s frustration grew and the visitors’ resolve increased – that magic pass or slice of luck needed to break through just didn’t look like happening.
Sergio Aguero and Kyle Walker were summoned off the bench for the last 15 minutes or so as the clock ticked towards what had looked like an unlikely draw before the game.
De Bruyne saw a free-kick well saved by Johnstone five minutes from time and then a break forward saw Aguero fire a powerful shot the wrong side of the post.
And in added time, De Bruyne's superb cross found Gundogan and his header from five yards was brilliantly saved by Johnstone.
Gundogan then fired a free-kick just wide but there was an even better chance as De Bruyne found Sterling a couple of yards out, but his point-blank header was again kept out by Johnstone in a frantic finish.
That was the last chance of a game that will be seen as a couple of points dropped by City.
"We should have won that game, but we can't change that now. We can do better, but it was not meant to be today.
"We can complain, but we cannot change it and must accept it. We have to look forward.
"It's nearly impossible to have just one team that's on top and dominating anything, especially with the schedule coming up.
"All teams in Europe are struggling to win games in a row. But we have responsibilities and we should win these kinds of games, especially at home.
"We deserved better, we had the chances. I don't know what to say, it's disappointing to get one point, we must win these kind of games."
Ilkay Gundogan's hard work and goal edged the star man vote on this occasion.
WHAT IT MEANS
City are sixth in the Premier League, five points behind leaders Tottenham Hotspur, but with six games to be played tomorrow night, that could change.
City travel to the south coast on Saturday to take on high-flying Southampton at St Mary's Stadium (kick-off 3pm).
"At the end we did everything but couldn't score a goal.
"We created enough to win the game, 26 shots I think, you just have to put the ball in, We are struggling with that. We have to be optimistic.
"We were there but unfortunately we could not score.
"We have dropped points - but we are in early December and there are a lot of games.
"We deserved to win the game but we didn't do it."
City: Ederson, Cancelo, Mendy (Walker 75), Ake, Dias, Rodrigo, Gundogan, De Bruyne (c), Foden (Aguero 75), Sterling, Jesus
Subs: Steffen, Laporte, Bernardo, Torres, Mahrez
West Brom: Johnstone, Furlong, Ajayi, O'Shea, Gibbs, Livermore (Krovinovic 80), Diangana, Gallagher, Sawyers, Phillips, Grant (Austin 70)
Subs: Robinson, Grosicki, Ivanovic, Peltier, Button
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