Liverpool goalkeeper Simon Mignolet went from zero to hero as Premier League leaders Chelsea were held to a 1-1 draw at Anfield, while Arsenal's title challenge was torpedoed by Watford's shock 2-1 win on Tuesday.
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.
Costa should have won it for Chelsea in the 76th minute when Joel Matip fouled him in the penalty area.
However, the Spain striker's spot-kick was pushed away by Mignolet as the keeper made amends for his earlier error.
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.
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 former Tottenham defender 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.
Alex Iwobi got one back for Arsenal when the young winger rammed home from Alexis Sanchez's cross in the 58th minute.
Gunners forward Lucas Perez hit the crossbar in the closing stages, but Watford held on for their first league victory at Arsenal since 1988.
Arsenal are nine points behind Chelsea in third place.