Cherries skipper David Brooks opened the scoring at Stamford Bridge after just six minutes before Cole Palmer restore parity from the penalty spot with 15 minutes on the clock.
Enzo Fernandez put the Blues ahead on 23 minutes, but the lead was short-lived as Justin Kluivert secured a share of the spoils with his 27th minute strike.
The result left Maresca's side in fifth place on the league standings with 30 points from 19 games - some 15 points adrift of leaders Arsenal - as the Cherries occupy 15th with 23 points.
Maresca was the victim of the boo-boys for his decision to replace Palmer with Joao Pedro just past the hour mark.
Chelsea really should have claimed all three points from this one though as Bournemouth arrived at Stamford Bridge without a win in nine.
But they took an early lead when Antoine Semenyo's long throw was bundled in at the second attempt by Brooks.
Semenyo, who is expected to be on his way to Manchester City, gifted Chelsea an equaliser for a trip on Estevao, that was easily dispatched by Palmer.
Fernandez then did well to beat his man before rifling a shot into the top corner of the Bournemouth goal, before
But another Semenyo throw caused all sorts of problems in the Blues box and Kluivert was able to sneak in at the back post to fire home.
Chelsea would go on to create just one clear-cut chance in the second half and ultimately extend their current run of form to one win in their last seven games.
After the game, Bournemouth boss Andoni Iraola said on Sky Sports: "I am very proud.
"It is one point, but we did very good things. We would have taken one point before coming here but looking at how the game developed I am probably not satisfied."
Chelsea coach Willy Caballero added: "Of course, any supporter wants to have their best players on the pitch and we want to have the best players on the pitch as well.
"But Cole is coming back from a long injury, in this case we need to also take the way to find the right substitutions to go for the game, and also to keep our players healthy because we want to have them for the rest of the season."
Chelsea next play Manchester City on Sunday, 4 January as Bournemouth face Arsenal a day earlier.