TALLINN, Estonia (AFP) - Wayne Rooney spared Roy Hodgson's blushes as the England captain's fine free-kick secured a 1-0 win against 10-man Estonia in a hard-fought Euro 2016 qualifier in Tallinn on Sunday.

Hodgson had taken a significant gamble by leaving out Raheem Sterling after he complained of feeling tired in training and England looked impotent without the teenage Liverpool midfielder for long periods at the Le Coq Arena.

Even after Estonia captain Ragnar Klavan was dismissed for a second booking early in the second half, Hodgson's side still laboured to see off the Baltic minnows.

But they finally made the breakthrough thanks to Manchester United striker Rooney, who curled home a free-kick with 17 minutes remaining to maintain England's 100 percent record after three Group E matches.

Rooney's moment of inspiration took him to 43 international goals - within one of Jimmy Greaves and only six behind record holder Bobby Charlton's tally of 49.

After winning their opening two qualifiers at a canter, Hodgson and his players had boldly declared their desire to win all 10 group matches. They remain on course to fulfil that ambition, but this was hardly the kind of dynamic display Hodgson would have hoped for from his youthful line-up.

Hodgson made three changes to the team that beat San Marino 5-0 on Thursday, with Sterling replaced by Liverpool colleague Adam Lallana, while Leighton Baines returned in place of Kieran Gibbs at left-back and Fabian Delph took over from James Milner in midfield.

The part-timers from San Marino barely made England break sweat in midweek, but Estonia, ranked 81st in FIFA's world rankings, represented a step up in class.

Even so, Hodgson had insisted England could have no excuses for failing to beat the unheralded hosts.

That warning didn't appear to have been heeded as Estonia threatened with less than a minute played when Sergei Zenjov saw his shot deflected into the side-netting before Henri Anier blazed over from the resulting corner.

Hodgson's team took a while to emerge from their shell after that tentative opening, but they went close when Rooney, winning his 99th cap, met Jack Wilshere's lofted pass with a volley that flashed just over.

He had a much easier chance moments later when a Baines cross found him unmarked at the near post, but Rooney was left holding his head in frustration after completely missing his kick.

Danny Welbeck's cross-shot was scrambled clear, Wilshere prodded into the side-netting and Rooney was off target with a header as England's lack of cutting edge ensured the first half petered out.

After a frustrating opening period, Hodgson's men received a welcome boost three minutes into the second half when Klavan was sent off following his second booking for a cynical block on Delph in central midfield.

Inevitably, Estonia responded to their skipper's dismissal by defending even deeper and, with less than half an hour to go, Hodgson moved to break the impasse by sending on Arsenal winger Alex Oxlade-Chamberlain for Delph and Sterling for Jordan Henderson.

Hodgson was looking increasingly agitated and the England manager's nerves were hardly eased when, with the goal at his mercy, Oxlade-Chamberlain mistimed his attempted header from Calum Chambers' cross.

But mounting England anxiety at the potential for an embarrassing result was finally quelled in the 73rd minute.

Sterling won a free-kick on the left edge of the Estonia penalty area and Rooney stepped up to score with a fine curling free-kick that goalkeeper Sergei Pareiko, despite getting both hands to the ball, could only push into the net via a post.

Rooney should have put a more flattering gloss on the scoreline in stoppage-time when he went through on goal, yet his erratic performance was summed up by a tame finish.