The Cherries took the lead inside the opening minute at the Vitality Stadium as Junior Stanislas gave them a perfect start to proceedings, but Jamie Vardy hit back in the early stages of the second half to level things up.
The 2015-16 champions were denied a place in the top 10 at the end of a largely difficult campaign, though, as Bournemouth held on to secure their best-ever league finish, ending the season ninth in the table.
Bournemouth went into the match having taken 10 points from the last 12 on offer, and they looked like continuing that good form when Stanislas stroked home the opening goal inside the very first minute after good work from Lys Mousset down the left flank.
It was Bournemouth's 100th goal in the Premier League and a third in as many games for Stanislas, but Leicester almost responded when Islam Slimani was close to applying a finishing touch to Christian Fuchs's flick-on at the back post.
It was the hosts who looked most like scoring for much of the first half, though, with Kasper Schmeichel being called into action to deny Dan Gosling midway through the opening period before the same midfielder was denied a tap-in by a last-ditch clearance moments later.
Ryan Fraser then tested Schmeichel at the end of another flowing move from the Cherries, but Leicester ended the half on top and Slimani saw one deflected strike fly narrowly wide before his glancing header from the resulting corner also missed the target by a whisker.
It took a point-blank save from Allsop to keep Bournemouth's lead intact going into half time after a Mahrez corner had dropped into the six-yard box, with the keeper preventing it from bouncing in off the back of Gosling.
Leicester started the second half as they ended the first and were rewarded with an equaliser within six minutes of the restart when Slimani nodded Ben Chilwell's delivery back across the face of goal for Vardy to tap in from close range.
Andrew Surman came close to restoring Bournemouth's lead with a low drive which flew just past the post shortly afterwards, but the Cherries were saved by the linesman's flag just before the hour mark when Vardy's goal was disallowed for offside following a one-two with Slimani.
The Foxes continued to push for a second goal and came close three times in quick succession when Vardy was denied by Allsop either side of an unmarked Slimani firing a volley wide of the target from inside the area.
Bournemouth were hanging on to the draw and saw a Wilfred Ndidi strike fizz just wide before Slimani squandered the best chance of the lot when he nodded Mahrez's cross off target after being left unmarked inside the box.
Leicester were also made to pay for that miss when Bournemouth broke up the other end two minutes from time, but Jordon Ibe's touch let him down when one on one with the keeper, allowing Schmeichel to come out and claim the ball.
That proved to be the final clear chance at either end as the two teams settled for a share of the spoils on the final day, with Bournemouth sealing ninth place and Leicester ending the campaign in 11th.