The start of the game was delayed by approximately 45 minutes due to traffic issues, as Sheffield had travelled up by road on Saturday morning, and had to navigate Bank Holiday traffic.
London made the stronger start, and Welsh international Rhys Williams opened the scoring with his 17th try of the season in the sixth minute.
But momentum swing back the other way in the 20th minute, when Nick Slyney too advantage of a good Scott Leatherbarrow kick, and some unfortunate handling from Eagles, to score. Wes Naiqama added the extras.
The Broncos conjured a try from nothing in the 28th minute, when Matt Garside touched down deftly after some magical handling and stepping from Williams. Garside touched down like a Super League winger, rather than a Championship back rower.
London extended their lead through Alex Foster, who scored his 10th try of the season in the 37 minute, after some clever running from Irish international Api Pewhairangi. The score at half time was Eagles 10-20 Broncos.
American international Mark Offerdahl put London further ahead after some incisive work with ball in hand from Jack Bussey. Naiqama once more added the extras, and it was beginning to look ominous for the Eagles at 26-10 to London.
Eddie Battye then went over under the posts, the former Sheffield prop bagging his second try of the season from close range in the 58th minute. Slyney was superb in the build-up.
Rob Worrincy offered some consolation with an 80 metre try after London dropped the ball in the Eagles 20m line. It was a fine finish, but a missed conversion from Aston, who looked frail all afternoon, meant that the Sheffield task looked too massive with less than seven minutes left.
So it proved, as London capped a dominant performance in the last few minutes by maintaining an impressive grip on the game.