Aston Villa remain third in the Championship after a 3-0 win at bottom club Sunderland, adding more pressure on the Mackems.
Lewis Grabban headed in against his old club on 34 minutes and James Chester nodded home a second from a corner just before the break.
An own goal by Sunderland midfielder Bryan Oviedo in the 66th minute completed the rout.
Fulham continued their own promotion charge with a 3-0 win over Sheffield United at Craven Cottage, where on-loan Newcastle frontman Aleksandar Mitrovic scored twice.
Mitrovic bundled in a low cross on 31 minutes for his fourth goal in as many games, and added another well-taken effort just before the break.
Tom Cairney knocked in a third after 61 minutes as Fulham made it 14 Championship games undefeated.
New Birmingham boss Garry Monk had a 39th birthday to forget as his first match in charge ended with 1-0 defeat by former club Middlesbrough at St Andrew's.
Patrick Bamford's close-range finish on 39 minutes proved enough for Boro, who move into a play-off position, while Blues remain in the bottom three.