Rovers led 8-5 at the interval and were three points clear until Reittie went over for what proved to be the winning try following a spell of sustained pressure 11 minutes from time
Ultimately though the difference between the sides was Dominic Brambani’s snap drop goal, booted after the half-time hooter sounded.
Batley, playing uphill, opened the scoring after 14 minutes when Reittie touched down after Shaun Squires had hacked on from Adam Gledhill’s kick.
Luke Briscoe grabbed a try from Anthony Thackeray’s kick to level the scores midway through the half and then James Duckworth crossed off Ian Hardman’s pass just before the interval.
Brambani landed his one-pointer with the final kick of the half, but Rovers scored first after the break through a Jamie Foster penalty.
That came after Dave Scott – who had been held up over the Featherstone line moments earlier – produced a try-saving tackle on Thackeray, but held on too long.
Bulldogs pulled two points back through a Pat Walker penalty moments later and thought they had gone ahead when Brambani stepped through the defence, but he knocked on trying to get the ball down.
Rovers held on to their three-point lead until Reittie went over for his second try, from Sam Smeaton’s outstanding pass.
Walker could not add the extras and Batley went closest to scoring again in the closing stages through Alistair leak’s long-range break.
Both sides went into the game looking for their first win.
Batley are now favourites to finish above Rovers on the middle-eights table, which would earn them an extra £50,000 in prize money.