Sears smashed the ball into the net from close range after just six minutes to edge Mick McCarthy’s side in front.
Luke Varney went close to extending the lead in the second-half but Blues were hanging on to the lead until Jones came off the bench to mark his debut with the equaliser eight minutes from time.
Town made three changes to the side that beat Watford before the international break, Zeki Fryers coming in for his debut for the suspended Tyrone Mings. Sears and Teddy
Bishop returned to the starting line-up, with Blues boosted by the presence of David McGoldrick and Jonny Williams on the bench.
Ryan Fraser headed wide from the game’s first opening for Bournemouth but it was Blues who made the early breakthrough, Daryl Murphy seeing his shot fall to Sears’ feet six yards out and the striker made no mistake.
The Cherries responded, Callum Wilson setting up Andrew Surman, who dragged his shot wide of the far post.
Surman then turned provider, his cross falling to Matt Ritchie, who found Brett Pitman but he couldn’t keep his effort under the bar.
Fryers blasted over at the other end after Varney tried to weave his way to goal, then Wilson was crowded out in an entertaining opening to the game.
Varney got on the end of Sears’ knock on but under pressure lifted the ball over the bar, Ritchie doing likewise at the other end.
Steve Cook had to get his tackle right on Sears as the Town striker got in behind him in the Cherries’ box, Luke Chambers unlucky to get a yellow card after he looked to have won the ball in a challenge with Fraser.
Pitman sidefooted straight at Bart Bialkowski after Bishop had lost possession inside his box, Cole Skuse then coming to Blues’ rescue after the Cherries had countered.
Tommy Elphick was at full stretch to head Murphy’s cross behind for a corner, then Bialkowski held firm to palm away Fraser’s strike after a flowing Bournemouth move, the Town ‘keeper forced into action a minute later to tip over Fraser’s cross.
Bialkowski palmed away another effort from Ritchie, Fraser’s follow up effort never threatening the Town goal as Blues went in at the break a goal up.
Sears pulled his shot wide as the second-half got underway, Town having a penalty appeal for handball waved away before Ritchie’s cross was cleared by Chambers.
Bialkowski held firm to deny Wilson and then Surman, then Fraser was thwarted by yet another Town block.
Ritchie saw another effort go wide before Richard Chaplow replaced Bishop just before the hour in Town’s first change.
Varney ripped a shot high and wide from distance as Blues looked for the crucial second goal, Yann Kermorgant coming on for Pitman as the Cherries changed things around up front.
The outstanding Christophe Berra cleared the danger again after Fraser and Wilson had linked up, Bournemouth making a double change for the closing stages, Adam Smith and Jones on for Fraser and Cook with Chris Wood on for Sears.
Varney was close to putting daylight between the teams, Artur Boruc denying the Blackburn loanee as he tried to lift the ball over the ‘keeper.
It proved to be a crucial save. Bournemouth hadn’t threatened from set-pieces until the 82nd minute, Ritchie’s corner found Jones who headed in from 10 yards to give the
Cherries a point and it needed a brilliant save from Bialkowski to keep out Kermorgant’s header in added time to prevent the Cherries leaving with all three.
Town: Bialkowski, Chambers, Smith, Berra, Fryers, Skuse, Tabb, Bishop (Chaplow 57), Varney (Clarke 89), Murphy, Sears (Wood 79). Subs not used: Gerken, Anderson, Williams, McGoldrick. Booked: Chambers.
Bournemouth: Boruc, Francis, Cook (Jones 78), Elphick, Daniels, Arter, Surman, Fraser (Smith 78), Ritchie, Wilson, Pitman (Kermorgant 66). Subs not used: Camp, Ward, Gosling, MacDonald. Booked: Arter.