Kompany connected with David Silva’s corner kick for the only goal in first-half stoppage time at the Etihad Stadium. City held on for a potentially title-deciding victory as it now leads United on goal difference.
City visits Newcastle United and hosts Queens Park Rangers in the remaining games, while United finishes against Swansea at home and Sunderland away.
After leading the Premier League for most of the season, City trailed United by eight points on April 8. But two more wins should be enough to claim a first league title since 1968.