The visitors wasted no time taking the lead, turning their early pressure into a goal from Gundogan, who settled a ball over the top of the West Brom defence, turned and fired home from just outside the penalty area.
Man City continued to dominate and added two more goals before the break, with Joao Cancelo scoring in the 20th minute before Gundogan added his second of the game on the half-hour to take his tally on the season to a personal Premier League best of seven.
Riyad Mahrez added further gloss to the scoreline in first-half stoppage time, cutting onto his right foot in the penalty area and beating West Brom keeper Sam Johnstone at the far post for a 4-0 lead at the break.
The onslaught continued in the second half as Man City got their fifth when Mahrez squared the ball across the West Brom goalmouth for the easiest of tap ins for Raheem Sterling.
City continued to spend much of the second half camped out on West Brom's side of midfield, but didn't add to their tally on the night as the match finished 5-0 in favour of Pep Guardiola's team, who have now won 11 straight in all competitions.
"The team, every game is there," said Guardiola, who was without key midfielder Kevin De Bruyne and striker Sergio Aguero but hardly lacked for attacking options.
"The way we play, everyone is involved in the attack and the play and creating chances and trying to score -- it doesn't matter, it is important to arrive in the box and create chances.
"Ilkay has the scent -- when he plays close to the box he has the scent to makes good runs and with quality on the ball he is always there."
The result puts City up to 41 points from 19 matches, one ahead of second-place Manchester United, while Sam Allardyce's West Brom remain mired in the relegation zone on 11 points.
West Brom winger Robert Snodgrass, making his home debut after a move from West Ham United, said they had to quickly bounce back.
"I'm here for the fight. We did everything we possibly could and I think if you look back at this, as a team, we'll realise that isn't good enough," Snodgrass said.
"We're not going to try and blame everyone else. We're going to take it on the chin and dust ourselves down. [There's] no hiding place in the Premier League, these top boys punish you."
The outcome makes City the ninth different side to end a day atop the Premier League this term, the most within a single top-flight campaign since 1986-87.