Connolly blasted home from the edge of the box to give the Black Cats an early lead but they were denied in added time when Femi Azeez scored.
Elsewhere, Finn Azaz bagged a brace in Middlesbrough’s 6-2 win away at Oxford, Mark McGuinness got the only goal as Luton beat Hull and Tom Cannon was on target for Stoke in their 1-1 draw with QPR.
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Championship round-up
Ten-man Sheffield United were unable to fully build on their lead at the top of the Sky Bet Championship as they were held 2-2 at Coventry.
Tyrese Campbell opened the scoring before Norman Bassette scored his first Coventry goal to level.
Jesurun Rak-Sayki put the Blades back in front before Anel Ahmedhodzic was sent off for grabbing Bassette by the throat and throwing him to the floor in a crazy rush of blood just before half-time.
Coventry piled on the pressure in the second half as Bobby Thomas headed Coventry level with 10 minutes remaining.
As a result Burnley were able to close in on them – with Leeds playing at Swansea on Sunday – thanks to a 1-0 win at Bristol City, earned by Jaidon Anthony.
Sunderland, though, were denied the same when Femi Azeez levelled three minutes into stoppage time as they drew 1-1 at Millwall in a game heavily delayed by medical emergencies in the crowd.
Aaron Connolly’s goal put the Black Cats ahead but they were unable to hold out.
Middlesbrough smashed six goals past Oxford to signal their intent to disrupt the order at the top.
Emmanuel Latte Lath scored a hat-trick, one from the spot, Finn Azaz a brace and Tommy Conway the other, with Greg Leigh and Dane Scarlett responding.
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Norwich are without a win in seven after they drew 2-2 at West Brom.
They went behind to Mason Holgate, but quickly led thanks to Emiliano Marcondes and an own goal from Torbjorn Heggem, but their lead lasted just two minutes before Josh Maja equalised.
Sam Greenwood and Jerry Yates traded goals as Preston and Derby drew 1-1, while a Ben Gibson own goal bailed out QPR as they drew 1-1 with Stoke. Tom Cannon give City the lead and Zan Celar missed a penalty for rock-bottom QPR.
At Hillsborough, Di’Shon Bernard’s first Championship goal for Sheffield Wednesday cancelled out Ollie Tanner’s opener as the Owls drew 1-1 with Cardiff.
At the foot of the table, Luton’s Rob Edwards emerged from the clash of under-pressure managers as his side beat Tim Walter’s Hull 1-0 thanks to Mark McGuinness’ goal. Hull are now in the relegation zone.