Rafael Benitez’s side were second best for long periods and have now scored only once in their last three matches, while Birmingham goalkeeper Tomasz Kuszczak made several excellent saves.
Fulham missed the chance to climb into the play-off places as they lost 3-1 at home to Wolves.
Ivan Cavaleiro gave Wolves a half-time lead and Andreas Weimann put them 2-0 ahead early in the second period.
Substitute Denis Odoi pulled one back for Fulham soon after, but Dave Edwards restored the visitors’ two-goal advantage.
Managerless Norwich halted their six-game winless run with a 2-0 home victory against Barnsley.
Jacob Murphy edged Norwich ahead just before the break and Angus MacDonald’s second-half own goal sealed Barnsley’s fate.
Aston Villa registered their fifth win in six league games with a 2-0 victory at struggling Wigan thanks to second-half goals from James Chester and substitute Scott Hogan.
Cardiff secured their first win in five with a 3-1 home victory over Ipswich, who had drawn their previous six.
Luke Chambers headed Ipswich into the lead, but Kenneth Zohore equalised before the break and notched his second soon after the restart before Joe Bennett added Cardiff’s third.
Brentford hit back from 3-1 down to win 5-3 at Burton, whose survival hopes were dealt a blow.
Marvin Sordell’s first-half double cancelled out Sergi Canos’ early opener for Brentford and Cauley Woodrow’s free-kick put Burton 3-1 up at the interval.
But Lasse Vibe struck twice after the break, either side of Canos’ second and Ramallo Jota added a late fifth for the Bees.
QPR condemned rock-bottom Rotherham to a seventh straight defeat with a 5-1 win at Loftus Road.
Matt Smith’s early goal was cancelled out by Rotherham’s Joe Newell, but Luke Freeman, Yeni Ngbakoto’s 49th-minute penalty – for Aymen Belaid’s foul on Smith – Massimo Luongo’s header and Nedum Onuoha’s late effort ensured another miserable afternoon for the visitors.
In a lunchtime kick-off at the City Ground, Daniel Pinillos’ stoppage-time header clinched Nottingham Forest a 2-2 draw against East Midlands rivals Derby.
Pinillos struck in the fourth minute of time added on to ensure both Forest boss Mark Warburton and Derby counterpart Gary Rowett, both appointed by their respective clubs on Tuesday, took a point from their first game in charge.
Derby pair Matej Vydra and David Nugent scored early in the second half to cancel out Zach Clough’s early opener for Forest before Pinillos’ last-gasp equaliser.
Aiden McGeady also scored a stoppage-time equaliser as Preston salvaged a 2-2 draw at local rivals Blackburn in another lunchtime kick-off.
Elliott Bennett and Craig Conway put Blackburn in front after Tom Barkhuizen had given Preston an early advantage and McGeady struck in the third minute of time added on.