Celtic cruised into the Scottish League Cup semi-finals with a 3-1 win over Kilmarnock at Rugby Park on Wednesday.

Gordon Strachan's side took the lead through Australia striker and Japan midfielder Shunsuke Nakamura added a superb free-kick to put the Scottish champions in control.

Killie striker Danny Invincibile pulled a goal back in the 67th minute but Aiden McGeady restored their two-goal lead to put the result beyond doubt.

Celtic join Rangers, Falkirk and Dundee United in the last-four draw.

Killie started brightly and within the first minute midfielder Mehdi Taouil tumbled in the box following a challenge from Mark Wilson but referee Craig Thomson was unimpressed by the penalty claims.

But as so often happens, the smaller club failed to capitalise on their good early work and in the 11th minute McDonald's header gave the visitors the lead.

Shaun Maloney's corner from the left was met by one of the smallest players on the pitch who guided the ball past Alan Combe from eight yards out.

In the 35th minute, as the game opened up, Invincibile twisted and turned at the edge of the Celtic box but his curled shot escaped Artur Boruc's left-hand post.

In the final minute of the half, after Grant Murray had fouled McDonald at the edge of the Killie box by clambering all over him, Nakamura curled the free-kick straight into the net to double the Parkhead side's lead.

Nakamura came off at half-time and his replacement Paul Hartley drilled a shot from 30 yards just wide with his first contribution to the game.

In the 67th minute, out of the blue, Kilmarnock gave themselves a lifeline when Invincibile pulled a goal back.

After the Australian was fouled by Gary Caldwell on the left, Taouil floated in the free-kick to the back post, Manuel Pascali headed back across goal and Invincibile bundled the ball over from a yard out.

But two minutes later any hopes of a fightback were extinguished. McGeady restored the visitors' two-goal lead when he took a pass from Scott Brown and slotted home.