* Third-placed City six points behind leaders Liverpool
* West Bromwich stay mired in relegation trouble (Adds details, quotes)
MANCHESTER, England, April 21 (Reuters) - Manchester City kept alive their flickering hopes of a second Premier League title in three seasons, and increased West Bromwich Albion's relegation worries, with a 3-1 victory on Monday.
Goals in the first 10 minutes from Argentines Pablo Zabaleta and Sergio Aguero and a third before halftime from compatriot Martin Demichelis, following a Graham Dorrans strike for the visitors, helped close the gap on leaders Liverpool to six points.
Third-placed City also have a game in hand on the top two clubs.
Liverpool, seeking a first English title since 1990, have 80 points from 35 games followed by Chelsea on 75 from 35 and City with 74 from 34.
City, whose title challenge had stalled with a defeat at Liverpool and a home draw with struggling Sunderland, face remaining games at Crystal Palace and Everton and home matches with Aston Villa and West Ham United.
"We talk with the players that if Liverpool win their (last) three games and win 14 games in a row then they will be the champions but our duty is to try to win our games and in that way Liverpool can feel pressure," City manager Manuel Pellegrini told Sky Sports.
City could face the prospect of being without influential Spanish midfielder David Silva after he was carried off on a stretcher with his right leg in a brace midway through the second half.
Pellegrini said Silva had an ankle injury but the extent of the problem would not be known until Tuesday.
"He has played the last three games with some pain in his ankle. Tomorrow we will have more news," said the Chilean. "We don't know if that pain has increased or if it is another problem."
City got just the start they needed in the third minute at a somewhat subdued Etihad Stadium when Aguero's strike was parried by keeper Ben Foster but the ball looped up and Zabaleta came flying in to head home.
Aguero doubled the advantage when he beat Foster from just outside the penalty area with a zipping shot that nestled in the bottom right corner.
The goals rocked Albion but they got one back on 16 minutes following a swift break that culminated with Dorrans showing fine skill and touch to control and then dink the ball past Gael Clichy on to his left foot before firing past keeper Joe Hart.
City, again missing midfielder Yaya Toure after he sustained a muscle injury in the Liverpool defeat on April 13, restored their two-goal lead 10 minutes before halftime when a corner was glanced on for an unmarked Demichelis to tap home at the far post.
West Brom, who remain fifth from bottom on 33 points, three points above the drop zone, carried little threat after the break with Morgan Amalfitano producing their best effort which forced Hart into a smart save. (Reporting by Justin Palmer; editing by Tony Jimenez)