Rovers threatened in the eighth minute, but Steven Reid saw his powerful strike from the edge of the box fly inches over the cross bar.
At the other end, Shire went close when Jordan Smith fired narrowly wide from almost 30 yards.
The home side made the breakthrough in the 18th minute when George Wallace drilled home from inside the box after being set up by Reid.
But Shire levelled just two minutes later when Andrew Brand converted a penalty after Andy Sim was adjudged to have fouled trialist Alan Patrick in the box.
Rovers almost restored their lead in the 32nd minute, but Gordon Lennon volleyed just wide from Reid's cross.
But the home side did find themselves in front on the stroke of half-time when Steven Noble blasted home after a Wallace cut-back broke kindly to him at the edge of the box.
Shire levelled in the 64th minute when trialist Patrick unleashed a quite sensational strike from 35 yards, but Rovers' debutant Sim restored their lead four minutes later with a fine solo effort before Reid added number four from close range in the 75th minute.