The visitors started the brighter, putting the Mowbray back four of Rudkin, Ward, Pole and Parker under pressure.
But it was Mowbray who had the best chance when Brighty was unlucky to see the ball bobble just as he struck his shot, sending it just over the bar.
Rangers kept attacking, but Oadby scored a fine counter-attacking goal leaving goalkeeper Bailey with no chance.
Further shots by Brown and Lomas went wide as the home side trailed going into half-time.
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The second half was mainly played out in the Oadby half with Barker strong in midfield and Henson showing good composure, but his deft finish went the wrong side of the post.
As the clock ticked down, the pressure finally paid off when Finch levelled with a shot which the keeper could not hold.
Mowbray camped in the Oadby box for the final five minutes, but could not bag a winner.