Ibrahima Bakayoko repaid a huge slice of his £4.5million transfer fee as Everton kept their season alive.

Bakayoko gave the Blues an undeserved lead four minutes from time when he fired a fierce 25-yard free-kick through the Bristol City wall and beyond Steve Phillips.

Then, with City pushing forward looking for an equaliser, Bakayoko ran onto Tony Grant's pass, beat Louis Carey and shot home via Phillips' body.

Before that, the Blues had had to withstand a second-half bombardment as the Robins belied their lowly position in Division One.

Everton will be hoping history repeats itself. When they last won the FA Cup, in 1995, they won 1-0 at Ashton Gate in the fourth round after being totally outplayed by their hosts.

And while the Blues were not under quite as much pressure today as they were four years ago, they enjoyed more than their fair share of luck.

Matthew Hewlett volleyed an Ade Akinbiyi cross against the post, while Akinbiyi - City's top scorer with 14 this season - missed two clear-cut openings in a minute as the Robins laid siege to Thomas Myhre's goal.

As the Blues' defending became more and more desperate, Ivan Tistimetanu went down in the visitors' penalty area after a tackle from Don Hutchison.

The assistant referee waved his flag furiously, presumably for a spot-kick, but ref Jeff Winter waved play on and Everton breathed again.

Had Walter Smith's side lost today, they would have had nothing but a relegation battle facing them between now and the end of the season.

But Bakayoko popped up at the right time to seal their place in round four with his fourth and fifth goals for the club he joined from Montpellier in October.

He was a doubtful starter but he overcame a hamstring injury to take his place in the side and just when Everton needed him most, he delivered the goods.

The Merseysiders have gone out of this competition to Division One opposition three times in the previous five seasons - to Bolton (1994), Port Vale (1996) and Bradford (1997).

And with other embarrassing exits in the League Cup to the likes of Millwall and York still painfully recent memories to Blues fans, they could have been forgiven for fearing they might be on the wrong end of a giant-killing.

Everton's problem this season has been a lack of firepower - they are the lowest scorers in the Premiership with 13 goals from 20 League games.

And while their defence was rarely troubled - though Adam Locke's third-minute drive flew inches wide of the post - their failure to first create and then convert chances was shown up in glaring fashion at Ashton Gate.

Phillips, 20, making only his sixth senior appearance, was called on just twice in the first-half, denying Don Hutchison and then Danny Cadamarteri.

Phillips' save from Cadamarteri was a superb effort, the Robins star diving low to his left to tip the striker's shot wide after Nick Barmby and Bakayoko had combined to carve open the hosts.

That was one of Barmby's few constructive contributions, the England international - still short of match fitness after 10 weeks out with a hernia problem - doing little before he was substituted after 58 minutes.

By then, though, Everton had started to come under more pressure, the Division One side starting to sense victory might be within their grasp.

Hewlett had a 25-yard shot saved by Myhre before he struck the post and Soren Andersen fired the follow-up effort over the bar.

If anything, Bakayoko and Cadamarteri had even less joy after half-time, the replacement of the influential Olivier Dacourt not helping the Blues as an attacking force.

As the game went on, City moved more and more on top, with Akinbiyi missing two gilt-edged chances in the space of 60 seconds.

First, he somehow managed to head Scott Murray's wonderful cross over from virtually underneath the crossbar with Myhre stranded.

And then, after the Everton keeper's goal-kick had gone straight to Akinbiyi, the striker's 20-yard shot flew harmlessly off target.

The Blues were clinging on by their fingernails but Bakayoko's first eased the tension among the visitors and then, as City threw more and more men forward, the Ivory Coast star sealed the win.

Teams:

Bristol City: Phillips, Locke (Goodridge 76), Bell, Murray, Shail, Carey, Hewlett (Hutchings 76), Tistimetanu, Akinbiyi, Torpey, Andersen.

Subs Not Used: Thorpe, Anderson, Dyche.

Booked: Akinbiyi, Goodridge.

Everton: Myhre, Ball, Dacourt (Grant 45), Watson, Unsworth, Barmby (Oster 58), Hutchison, Bakayoko, Dunne, Bilic, Cadamarteri (Branch 81).

Subs Not Used: Cleland, Simonsen.

Booked: Ball, Unsworth, Bilic.

Goals: Bakayoko 86, 88.

Att: 19,608

Ref: J Winter (Stockton-on-Tees).