Simon Francis was dubiously given his marching orders by Andre Marriner in the second half for a tackle on Leicester's Jamie Vardy in the penalty area.
But Artur Boruc was on hand to save the resulting spot kick and ensure the Cherries took a share of the points from their first match of 2016.
Eddie Howe's men enjoyed a very positive start at King Power Stadium. Early attacks down the left through Charlie Daniels and Junior Stanislas saw the Leicester City defence constantly tested, but the hosts remained resolute.
Joshua King then had the chance to take the lead on the 13th minute. A deep cross from Simon Francis was cut back by Stanislas on the byline, but King’s header from inside the six-yard box whistled just past the far post.
The hosts then had a chance of their own through Jamie Vardy. Leonardo Ulloa slipped the in-form striker in on goal but his shot from close range bounced off the post and clear.
Apart from that chance it was all AFC Bournemouth in the first half. And Stanislas fired narrowly over the crossbar on the half-an-hour mark after a smart ball from Matt Ritchie.
King then took on Huth down the right flank before cutting back and teeing up the on-rushing Dan Gosling, but his shot flew over the crossbar too.
The home side soon responded as Vardy was released into the Bournemouth penalty area. The striker got caught in two minds, however, and his eventual cross-come-shot caused Boruc little trouble.
Vardy then had another chance to open proceedings early in the second half, but his drilled effort from the edge of the penalty area was tipped away by Boruc.
At this point Eddie Howe made his first change of the afternoon, as King was replaced by Glenn Murray on the 50 minute mark.
The big action of the half came shortly after. Arter was hauled down inside the Leicester half, leaving Vardy to break the Cherries offside trap and surge forward one-on-one with Boruc.
Francis recovered well though and put in a tackle to deny the Leicester striker, but referee Andre Marriner adjudged the captain’s tackle to have been mistimed. Awarding Leicester a penalty and giving Francis his marching orders.
Mahrez stepped up to convert from the spot, yet the Algerian was denied by a strong right hand from Boruc who correctly guessed the right way.
With just ten men AFC Bournemouth had to dig deep, as Leicester continued to threaten through Okazaki and Vardy.
The latter again went down in the penalty area in the dying moments of the match, but this time he was waved to his feet by Marriner.
Leicester: Schmeichel, Drinkwater, Morgan, Huth, Vardy, Albrighton (Okazaki, 65), Kante, Simpson (De Laet, 73), Ulloa (Dyer, 45), Mahrez, Fuchs.
Subs not used: King, Wasilewski, Schwarzer, Inler.
Cherries: Boruc, Daniels, Cook, Francis, Smith, Gosling, Arter (Distin, 60), Surman, Ritchie, Stanislas, King (Murray, 50).
Sent off: Francis
Subs not used: Federici, Tomlin, Rantie, Pugh, MacDonald
Attendance: 32,006 (2,206)