The win puts the Blues two points adrift of fourth-placed Spurs in the Premier League and halts successive league defeats.
Antonio Conte said Chelsea can not afford to drop any more points in the race to finish in the top four, as the Blues shook off a run of four league defeats from five to beat Crystal Palace at Stamford Bridge.
Speaking ahead of the Crystal Palace game, Conte spoke about his attacking options, improvements needed in that department and the need to reduce the mistakes which have been plaguing us in the past few weeks. They dominated the ball and had seven attempts at Wayne Hennessey's goal in the opening 20 minutes, albeit without truly testing the Palace goalkeeper.
"The second half was much better - I thought that we were more aggressive and pushed up better from the back and played as we'd hoped to right from the first whistle".
But although Chelsea continued to make most of the chances, Zaha's arrival had boosted Palace.
Cesc Fabregas began it with an inch-perfect pass out to Marcos Alonso on the left.
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Hodgson saw his Palace side beaten 3-2 at home by Manchester United on Monday and conceded the third in stoppage-time to remain in the bottom three.
Antonio Conte was a manager under pressure before this match, as much because of his perceived pessimism over his team's prospects as their results.
Wilfried Zaha (knee) and Mamadou Sakho (calf) will both undergo late fitness tests but Joel Ward, Scott Dann, Yohan Cabaye, Ruben Loftus-Cheek, Jason Puncheon, Bakary Sako, Connor Wickham and Julian Speroni are all out.
Luckily Martin Kelly was on hand to stop the shot with a goal-line clearance.
Upon the visit of Crystal Palace to Stamford Bridge, nothing short of victory would do for Chelsea. But with Palace offering little going forward in the first half, Hodgson brought the 25-year-old on at the break, and his impact was immediate. Then Patrick van Aanholt struck cleanly but straight at Courtois. Zappacosta gave a poor pass to Christensen who, lost the ball to Alexander Sorloth who raced clear.
They were excellent against Barcelona though and were unfortunate not to win that game, and will have one eye on Wednesday's return leg. Worked well with Willian and Hazard and overall looked a better proposition as a target man than Morata who replaced him late on.