Bottom of the table Livingston were held by Inverness at Almondvale.
Livingston are still looking for win in the SPL
Defender Harald Pinxten volleyed home Richard Brittain's left-wing corner on 13 minutes - just Livi's third league goal of a miserable term so far.
Graham Barrett missed a couple of chances to extend the home side's advantage, while Dennis Wyness wasted a good opportunity for Inverness.
But Alan Morgan drew the visitors level after 71 minutes when he flighted in a great free-kick from 20 yards.
Livingston remain at the foot of the table although the draw does take them to within two points of Dunfermline, who lost at Hearts.
And luckless Livi played the final 13 minutes of the match with just 10 men when, with all three substitutions used, they lost Barrett to what appeared to be a serious injury.
Livi started well and went close when Robert Snodgrass pounced on a bouncing ball and forced keeper Mark Brown to tip over.
From the resulting corner, Brittain crossed for Pinxten to arrive unmarked in the box and smash the ball home.
Livi continued to play the better football and, in the 25th minute, Snodgrass unselfishly teed up strike partner Barrett inside the box but the finish lacked composure as he blasted over.
Ten minutes before the interval Barrett connected with Paul Tierney's cross to head just over.
Pinxten would have grabbed another goal but for a fine save from Brown, who then denied Snodgrass with the follow-up.
Liam Fox forced Roddy McKenzie into a fine save and from the subsequent corner Barry Wilson fired a dipping shot just over - Inverness' only threat in the first 45minutes.
Inverness improved after the interval and Fox's snapshot crept just outside the post.
And Dennis Wyness wasted an excellent chance to equalise when he found himself unmarked in the box but could only side-foot wide from eight yards.
The visitors were level when left-back Morgan curled in a fine free-kick, although McKenzie looked slow to react.
The home side were reduced to 10 men with 13 minutes left when, with all their substitutions used, striker Barrett was carried off on a stretcher.
The visitors dominated remainder of match and, although Wilson again went close with a side-footed effort and Morgan fired an injury-time free-kick just wide, they could not find a winner.
Livingston: McKenzie, Mackay, Pinxten, Strong, Tierney, Dair (Adam 39), Brittain, Adams, Walker (Neil Barrett 61), Snodgrass (Scott 66), Graham Barrett. Subs Not Used: Roy, Boyd, Pereira, Miller.
Booked: Pinxten, Mackay, Strong. Goals: Pinxten 14.
Inverness CT: Brown, Tokely, Dods, Munro, Morgan, Hart (Proctor 71), Fox, Duncan, Wilson, Brewster, Wyness. Subs Not Used: Fraser, Bayne, Hastings, Dargo, Parratt, Black.
Booked: Fox. Goals: Morgan 72.
Ref: M Ritchie