Alonso opened the scoring in the 33rd minute with a crisp strike after Olivier Giroud struck the crossbar with an acrobatic flick, but Chelsea was punished for dwelling on that lead. Bournemouth scored twice in a three-minute span from the 54th, Jefferson Lerma thumping in a header from a corner before Josh King tapped in at the far post following a low cross from Jack Stacey.
Alonso scrambled in the equalizer in the 85th, though, and the draw lifted fourth-place Chelsea four points ahead of fifth-place Manchester United having played a game more. United visits Everton on Sunday and they are two of the eight teams within nine points of Chelsea.
A 10th league defeat of the campaign would have opened the door for Chelsea to drop out of the top four for the first time since October, having seemingly consolidated the position by beating Tottenham 2-1 last weekend - when Alonso scored on his first start in two months.
Bournemouth remained just outside the relegation zone with 10 games left.
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