Bournemouth 1-3 Liverpool

Raheem Sterling scored his first Liverpool goals since September

• Sterling scores either side of Markovic strike

• Liverpool face Chelsea in semi-finals

• Third win in 11 matches for Liverpool

• Bournemouth suffer first defeat in 13 games

Liverpool set up a League Cup semi-final meeting with Chelsea as Raheem Sterling scored twice to see off Championship leaders Bournemouth.

The makeshift striker nodded in the opener after Callum Wilson missed a glorious chance to put the hosts ahead.

Lazar Markovic's precise finish doubled the lead, but the Reds were thankful for Yann Kermorgant's glaring miss.

Sterling stroked in after the break and, although Dan Gosling bundled in to set nerves on edge, the Reds held on.

The victory should provide a shot of confidence for a Liverpool side that had won only two of their previous 10 games and face an in-form Arsenal in the Premier League on Sunday.

It was a welcome boost for Liverpool manager Brendan Rodgers, who has come under pressure following his team's poor start to the season and last week denied reports of dressing room unrest.

Sterling's brace was the first time he has found the net for his club since September and, after missing a succession of chances in last weekend's 3-0 league defeat by Manchester United, he looked more composed in a new central role.

With Liverpool 11th in the Premier League and Bournemouth topping the Championship on the back of a 12-match unbeaten run, only 10 league places separated the sides at kick-off.

But, after Wilson stabbed wide with only goalkeeper Brad Jones to beat, the visitors made that narrow gap feel like a chasm in class.

Liverpool dominated possession and had threatened through Adam Lallana and Steven Gerrard's crisp long-range strikes when Sterling capped a 52-pass move with the opener.

Sporting a newly shaved head, the 20-year-old stooped to glance home a close-range header after Markovic's deep cross had been nodded into the six-yard box by Jordan Henderson.

Liverpool's second goal stemmed from Bournemouth defender Tommy Elphick turning his back on Philippe Coutinho, apparently distracted by a whistle from the crowd.

The Brazilian's shot was blocked by goalkeeper Artur Boruc, but the ball ran to Markovic, who thumped a half-volley through a forest of legs and into the bottom corner from 15 yards.

Bournemouth's Simon Francis burst down the right and squared for Kermorgant, but the Frenchman blazed over with the goal gaping and under little pressure.

With the Bournemouth defence pushing a higher line after the break, England international Sterling exploited the space in behind, twisting and turning Elphick before rolling home a composed finish.

Liverpool were briefly shaken when Matt Ritchie's cross was ushered past Martin Skrtel and Kolo Toure by former Everton player Gosling, whose shot beat an unconvincing Jones.

Although Gosling hit the upright with a curling effort, Liverpool closed out the game in relative comfort.

Bournemouth boss Eddie Howe: "We showed our quality, showed we can create chances against a good team, but you have to admire their quality - they have world-class players.

"We were too open and got caught between two stools, of pressing and getting a good block on.

"We tweaked things at half-time - we took a risk with two strikers but we wanted to be positive. We were at home in a cup tie and wanted take the game to Liverpool to give it a go."

Liverpool boss Brendan Rodgers invited Bournemouth counterpart Eddie Howe to watch his training sessions while in charge of Swansea

Bournemouth were left to rue two wasted first-half opportunities

Lazar Markovic scored his first goal for Liverpool since his £20m summer move from Benfica

Brad Jones continued in the Liverpool goal in place of Simon Mignolet