United, who had won eight of their last nine games prior to kick-off, came roaring out of the blocks and Paul Paton fired them in front before McGinn nodded in a second-half equaliser.
Aberdeen skipper Russell Anderson could only divert Brian Graham’s low cross to Paton (6) and an assured side-foot finish from 20 yards did the rest.
United were in the mood and John Rankin’s long-range effort had Aberdeen goalkeeper Jamie Langfield at full stretch.
John Souttar was the next to threaten, his close-range drive being deflected behind.
McGinn rose to meet Shaleum Logan’s cross but could not get enough power on his header while Graham was soon working Langfield at the other end.
Radoslaw Cierzniak produced a fine save to keep out Barry Robson’s shot before McGinn’s first goal in 18 games brought Aberdeen level, as he headed in Robson’s cross from close range (52).
Adam Rooney’s turn and shot failed to reap dividends and Ryan Jack blazed over but the home side were happy to settle for the draw that kept them five points clear of United.