England laboured to victory over Estonia in Tallinn as Wayne Rooney's late free-kick made it three wins out of three in their Euro 2016 qualifying campaign.

Rooney curled his shot in from just outside the area 17 minutes from the end of a mediocre encounter to give England's captain his 43rd goal for his country – six behind all-time record holder Sir Bobby Charlton.

It rescued England as they struggled to break down the stubborn Estonians, who stood firm even after captain Ragnar Klavan had been sent off for a second yellow card three minutes into the second half.

And it spared manager Roy Hodgson some awkward questions over the omission of Raheem Sterling after Liverpool's teenager admitted he was tired following the 5-0 win against San Marino at Wembley.

England monopolised possession but the lack of end product was alarming against opponents who were dogged but hardly an upgrade into the European elite after the stroll against San Marino on Thursday.

Rooney's winner, a rare touch of class, also lifted his own performance after the 28-year-old struggled to apply his usual high standards. Indeed he was in danger of being replaced by Rickie Lambert just before his decisive contribution.

England coach Roy Hodgson

Hodgson was buoyant after his side maintained their 100% record against San Marino on Thursday

The Manchester United captain had opportunities before and after his goal to move closer to history but his display was in keeping with England's night – largely frustrating and salvaged only by a single moment.

Hodgson used the diamond formation, as he had in the opening 2-0 win against Switzerland in Basel, but whereas there – with Sterling at its point – it looked effective, here it left England lacking in pace, creation and width. It was only when Arsenal's Alex Oxlade-Chamberlain and the Liverpool youngster were introduced that England looked like getting behind the hosts.

They can justifiably point to a job done, and nine points out of nine, but this largely uninspired fare did little to warm fans who turned out in plummeting temperatures in Tallinn.

There should be few obstacles in England's way on the route to Euro 2016  – the possibility of 10 wins remains a strong one – but it is to be hoped the level of excitement is greater than that witnessed here in a group not exactly sprinkled with stardust.

After a minor scare in the opening seconds, England dominated the first period to such an extent that one point they enjoyed an 82% share of possession – the more telling statistic was that they did not muster a shot on target until the dying moments of the half.

This had much to do with Rooney's failure to accept chances, volleying over from Jack Wilshere's pass and showing an uncharacteristic lack of control and sharpness in the area when given other opportunities.

The visitors were looking for any advantage they could get and one arrived three minutes into the second half when Klavan departed after a cynical barge on Fabian Delph.

Hodgson made two changes in quick succession just after the hour as Oxlade-Chamberlain and Sterling replaced Delph and Jordan Henderson.

And Sterling was involved as England finally broke Estonia down after 73 minutes. He was fouled on the angle of the penalty area and Rooney weighed his options up carefully before curling in a low, right-foot effort from the set-piece.

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