An early Kidlington goal meant Rovers' unbeaten league start came to an end.
Rovers made one change from Saturday's win against FC Romania, Emmanuel Dahie coming in for the injured Rafal Wielblad who suffered mild concussion during the previous fixture.
Rovers had the first chance and was a big one, Baker beating his man on the right and he drilled his cross across the six yard box where Hatch was waiting, however the Kidlington goalkeeper reacted extremely well to stop the ball crossing the line.
The save was crucial as just three minutes later the visitors took the lead, a cross from the left found Ryan Knight to slot home from ten yards as he found space in the box.
Rovers were knocking on the door after the early goal, forcing the visitors into mistakes which led to chances, however the best chance fell to Baker who dragged his shot ever so slightly wide.
Into the second 45 and the visitors had the first chance of the half, George Rose pulling off a superb fingertip save to divert a curling shot onto the crossbar.
Shortly after Rovers were forced into two changes, firstly Harry Riley making way for Perry Ronayne followed by Jake Kerins making his home debut in place of Magloire Muyembe.
On 64 minutes Baker had a chance to equalise, Stevens and Dahie linking well on the left before Hatch found Baker out wide, his shot was well saved by the Greens' goalkeeper.
Rovers unfortunately failed to equalise, Stratton and Hatch had half chances but the visitors defended well and did their job excellently.
The Walnuts slip to third as Kidlington leap above us into second. Next up we travel to Aylesbury Utd this Saturday.