SPL Wrap: Ross County battle to earn derby draw
Marley Watkins put hosts Inverness in front with a fine curling strike seven minutes before the interval.
But John Hughes' third-place side were unable to fully capitalise on top two Celtic and Aberdeen being in League Cup semi-final action this weekend as Gary Warren put through his own goal in the 76th minute.
Ross County remain six points adrift at the foot of the table after second-bottom Motherwell secured a 1-1 draw at home to St Johnstone despite Louis Laing's red card.
Murray Davidson slotted home to give St Johnstone an early lead and the Fir Park faithful would have feared the worst after 25 minutes when last-man Laing brought down Chris Kane.
However, Motherwell produced a stirring second-half display and John Sutton rifled in his seventh goal of the season 15 minutes from time.
Dundee and Hamilton Academical completed a trio of 1-1 scorelines amid late drama at Dens Park.
Hamilton avoided a fifth consecutive defeat despite having Dougie Imrie sent off for an altercation with Greg Stewart.
It could have been even better for the visitors as player-manager Martin Canning headed them into an 85th-minute lead but Stewart responded three minutes later.