At the Tottenham Hotspur Stadium, Bournemouth missed a chance to climb into the top four race as the hosts saved boss Ange Postecoglou from another defeat.
Tottenham lost 1-0 at AZ Alkmaar in the Europa League last 16 first leg on Thursday.
That competition represents Tottenham's last chance of fulfilling Postecoglou's boast that he always win a trophy in his second season.
Languishing in 13th in the Premier League, Postecoglou's side have gone three games without a win in all competitions.
Tottenham striker Dominic Solanke shook off a back injury for his first league appearance since January, while Cristian Romero returned to the Tottenham defence for the first time since December after a thigh injury.
Despite those reinforcements, Tottenham conceded in the 42nd minute, when Marcus Tavernier applied the finishing touch to Milos Kerkez's pin-point cross after Pedro Porro carelessly conceded possession.
Postecoglou sent on Son Heung-min at half-time in a bid to spark Tottenham and the South Korean was inches away from equalising as his deflected strike whistled wide.
Bournemouth struck again in the 65th minute as Evanilson raced onto Justin Kluivert's pass and lifted a composed finish over Guglielmo Vicario.
But Pape Sarr reduced the deficit two minutes later, the Tottenham midfielder catching out Bournemouth keeper Kepa Arrizabalaga with a misjudged cross that somehow dipped in at the far post.
Tottenham completed their escape in the 84th minute as Kepa conceded a penalty with a desperate lunge on Son.
Son calmly slotted home from the spot for his first goal in 10 games, taking him to 11 in all competitions this season.