Sunderland are still not safe after losing 2-0 at Newcastle United in the day's second derby, Michael Owen scoring twice for Kevin Keegan's resurgent side at St James' Park.
Birmingham are third from bottom with 31 points, one behind Reading who sit just above the drop zone. Sunderland have 36.
Owen needed just four minutes to head Newcastle in front and he doubled the advantage from the penalty spot before halftime to make it six goals in six games for the England striker.
Sunderland improved after the break without really threatening a comeback.
Earlier on Sunday, Aston Villa thrashed local rivals Birmingham City 5-1 to take their goal tally to 15 in their last three Premier League games.
John Carew and Ashley Young both scored twice for Villa to leave City stuck in the relegation zone with three matches left to save themselves.
Gabriel Agbonlahor was also on target for the home side while Mikael Forssell scored a consolation for an outclassed Birmingham side who have 31 points, one behind fourth from bottom Reading.
Villa's victory put them three points behind fifth-placed Everton and increased their chances of qualifying for next season's UEFA Cup.
FA Cup finalists Portsmouth had the chance to close the gap on Everton to one point but they failed to win at Manchester City.
Goals from Darius Vassell, Martin Petrov and Benjamin Mwaruwari ensured Sven-Goran Eriksson's side a 3-1 win. John Utaka scored the lone goal for Portsmouth.