But substitute Michy Batshuayi equalized with his first goal for Chelsea since his £33m move. Then Costa ran on to substitute Cesc Fabregas' pass and slid the ball under Heurelho Gomes with three minutes left.
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The33-year-old singer is now gearing up to release her seventh album Beauty Marks, the follow-up to 2015's Jackie, on May 10 featuring collaborations with Macklemore and Kelly Rowland.
The33-year-old, who has suffered a dip in form recently, then fired Newcastle's second penalty wide and once keeper Djordje Petrovic saved Matt Ritchie's spot-kick Chelsea had gone from the despair of contemplating defeat to the sheer elation
The33-year-old former England keeper also tipped over a fizzing shot from Sanchez before West Brom nearly snatched a goal, with Claudio Yacob skying his shot over the bar after Arsenal keeper Petr Cech dropped a corner.
The result leaves Mikel Arteta's Gunners second in the table, two points behind league leaders Liverpool, while West Ham end the year with 33 points - their highest total at the halfway stage in a Premier League campaign.
The visitors kept out their opponents for 33 minutes with some determined defending but City always looked capable of going through the gears and they opened the scoring when Foden drove home from inside the box after Alvarez's shot was blocked