United's first attack of note brought them the opener after seven minutes when Scott Smith played the ball through to Mark Millar who drilled in a low shot from 12 yards.
Only a tremendous save by Joe McGovern, when he tipped over Kyle MacLeod's powerful header, prevented County levelling after 14 minutes.
But the equaliser was only delayed a couple of minutes because MacLeod played in Darren Maatens and the Dutchman's angled drive from 14 yards found the far corner.
Midway through the half, MacLeod was lucky to only be booked for a reckless challenge which resulted in United's Darren Petrie limping off.
Although the hosts continued to dominate, it was the Tangerines who led at the interval when Jamie Montgomery latched on to Scott Fraser's through ball and fired a right-foot shot high into the net from the corner of the penalty box.
United started the second half with Chris McLaughlin on off Mark Russell who replaced the unfortunate Petrie.
County forced a good save by McGovern from Tony Dingwall's 25-yarder after 57 minutes as County chased an equaliser.
And MacLeod was only a whisker away with a snap-shot that went inches past midway through the second half. But with 20 minutes left, he was more successful controlling a Dingwall pass before scoring with a shot on the turn from 12 yards.
But United's tenacity won the day with 12 minutes left when Scott Smith smashed a shot into the top right-hand corner from the edge of the box.
Dundee United: McGovern, Gilmour, Spark (Ballantyne 82), Petrie (M Russell 23 (McLaughlin 46), Harwood, Hendry, Millar, Oyenuga, Fraser, S Smith.
Sub not used: Tumilty.