Antonio Conte's Chelsea grabbed the lead in the 25th minute when David Luiz cheekily took a quick free-kick that flashed past Mignolet, who was caught out while he lined up his defensive wall.
Mignolet looked bewildered that the Brazil defender's effort wasn't ruled out, but referee Mark Clattenburg allowed Luiz to celebrate his first goal since rejoining Chelsea from Paris Saint-Germain in August.
Georginio Wijnaldum came to Liverpool's rescue as the midfielder equalised with a 57th minute header from James Milner's cross.
However, the Spain striker's spot-kick was pushed away by Mignolet as the keeper made amends for his earlier error.
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For just the second time in their last 17 leagues games, Chelsea finished without three points, but the Blues are still nine points clear of second placed Tottenham.
"It's a pity Diego missed the penalty, but we must be happy with the result and the performance because it is not easy to play away at Liverpool,"Conte said.
Fourth placed Liverpool, 10 points behind Chelsea, have only won one of their last nine matches in all competitions, but their battling display at least partially eased the pain of Saturday's FA Cup embarrassment against second tier Wolves.
At the Emirates Stadium, Arsene Wenger was again watching from high in the stands as he served his touchline ban and the Arsenal boss was rocked in the 10th minute when Younes Kaboul's powerful strike deflected in off Aaron Ramsey.
Watford suffered an embarrassing FA Cup defeat at third tier Millwall on Sunday and had gone seven league games without a win.
But the view from the posh seats got even more uncomfortable for Wenger three minutes later as Troy Deeney doubled Watford's lead with a close-range finish after Etienne Capoue unhinged the Arsenal defence.
in which they had scored first this season, Newcastle always looked capable of coming back.
After spurning a series of chances, the visitors luck changed as they drew level in the 81st minute.
Christian Atsu's miscued shot spun off Diame and looped into the air, eluding Brighton goalkeeper David Stockdale as it went into the top corner.
Atsu was the catalyst for a more conventional Newcastle when he got clear down the left in the 89th minute and crossed for Perez to side-foot home from 10 yards.
- Jeered -
Jonathan Kodjia went from zero to hero against his former club as Aston Villa eased their relegation fears with a 2-0 win over Bristol City at Villa Park.
Kodjia joined Villa from City last year and the striker was jeered by the away fans after crashing a first-half penalty against the crossbar.
However, the Ivorian scored Villa's 54th minute opener and then set up Conor Hourihane's first goal for the club in the 59th minute as Villa put nine points between themselves and a struggling City side now without a win in their last five.
Struggling Blackburn marked new manager Tony Mowbray's first home game with a 1-0 win over Derby that improved their survival prospects and dented their visitors' play-off push.
Blackburn's winner came via a Craig Conway penalty in the 58th minute, moving them level on points with 21st-placed Bristol City.
Derby, now without a goal in three games, have ended a winless February languishing 10 points behind the top six.