Fire crews were called to the property, in Woodburn Road, Stourport-on-Severn, shortly after 4am on Wednesday after the flames were spotted by a passing motorist.
The driver and his passenger phoned 999 and knocked loudly at at the door to alert the 94-year-old resident.
West Mercia Police then launched an appeal for information, resulting in the two children coming forward to assist with their investigations.
The force has now praised members of the community for its response after an appeal for security camera footage in a bid to track down the culprits.
Its website stated: "Following this widespread appeal, two children from Stourport came forward and were interviewed by officers as part of a joint investigation by Kidderminster police and Stourport Safer Neighbourhood Team.
"Due to the ages of those who came forward our youth offending teams are now working on a resolution."