Rooney curled his shot in from just outside the area 17 minutes from the end of a mediocre encounter to record his 43rd goal for his country, six behind all-time record holder Sir Bobby Charlton.
Rooney's striker 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 that he was tired following the 5-0 win against San Marino at Wembley.
Rooney's winner, a rare touch of class, lifted his own performance after the striker struggled to apply his usual high standards. Indeed he was in danger of being replaced by Rickie Lambert just before his decisive contribution.
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.
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 there in a group not exactly sprinkled with stardust, the report added.