Nuno Espirito Santo's side moved two points clear of Sheffield United who beat Burton Albion 3-1 on Friday.
Cardiff ensured they kept the pressure on the top two as goals from Joe Ralls and Danny Ward helped the Welsh club record a 2-0 home win over Brentford.
Fourth-placed Bristol City had to settle for a point as they drew 0-0 with Sheffield Wednesday while Aston Villa kept their promotion hopes alive as they came from behind to beat QPR 2-1 at Loftus Road.
Sunderland created history for all the wrong reasons as they became the first league team in English football to fail to secure a victory in 20 consecutive home games in all competitions.
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The north-east club took an early lead against Millwall, but two goals from George Saville put the London club in pole position and Sunderland needed an early second-half strike from Adam Matthews to help salvage a point.
Birmingham City moved out of the relegation zone as they claimed their first win in four games with a 1-0 win over Nottingham Forest.
Hull City failed to move clear of the bottom three as they were held to a 2-2 draw by Ipswich Town while Norwich City and Barnsley had to settle for a point following the 1-1 draw at Carrow Road.
(Editing by Ed Osmond)
