John Deacey's men fell behind after just four minutes, Harry Winter teeing up Liam Ellis to slip a neat finish under Boro custodian Tommy Taylor to give the hosts an early lead.
Boro's first opportunity on the hosts' goal came on 12 minutes, Chris Dawson firing an effort over the bar.
The visitors almost levelled in bizarre circumstances in the 19th minute when Kingsley Williams sliced an attempted clearance towards his own goal, but keeper Ollie Martin reacted to push the ball onto the bar and away to safety.
Boro began to threaten the Radcliffe goal and Martin was forced into two smart saves to keep the visitors at bay, the second to keep out skipper Michael Coulson's low drive.
However, Deacey's men weren't to be denied for much longer and in the 39th minute James Walshaw cut inside and fired a thunderous strike into the bottom corner to send the sides in level at the break.
Radcliffe soon regained the lead though, a mix up in the Boro defence allowing Kingsley Williams a simple tap in for 2-1.
Boro introduced Ryan Watson and Jack Johnson returned from a lengthy spell on the sidelines as the visitors looked for a way back into the contest.
It wasn't to be for the visitors though and Ben Wharton slotted home a stoppage-time penalty after Wayne Brooksby was adjudged to have brought down a home player in the box, wrapping up a disappointing afternoon for Boro.