A fine David Robertson strike saw the Tangerines edge out their Caley Thistle counterparts as the reserves returned to action after the winter break at the Tulloch Caledonian Stadium.
Both sides fielded strong sides United held the upper hand in terms of possession before going in front after the 34 minutes.
Ryan Dow cut inside from the left skipped past three challenges along the 18 yard line before firing a low shot into the bottom corner.
But for Michael Fraser, the Taysiders would have gone in two ahead with the keeper turning a David Goodwillie round the post five minutes from the break.
However, within a minute of the restart, the home side were level.
Richie Byrne and Roy McBain combined well down the left side before Byrne crossed with Garry Wood supplying the neat finish.
Four minutes later, the Highlanders went close after a free-kick from Thierry Gathuessi was flicked on by Wood to the back post, but Adam Rooney' poked his effort the wrong side of the post.
But on the hour mark, United regained the lead. David Goodwillie found midfielder David Robertson 20 yards out from goal and had time to pick his spot, drilling a low shot into the bottom corner.
Inverness CT: Fraser, Gathuessi S. Sutherland 70), McGuire, Hastings, Byrne, Leslie, Kerr (Scott-Woodhouse 63), McBain (Morrison 63), Vigurs, Wood, Rooney. Subs not used: Allison, Hemsley.
Dundee United: McGovern, Milligan, Kovacevic, Dillon, Dixon, D Robertson, Cameron (Ross McCord 80), Swanson, Shala, Goodwillie, Dow. Subs not used: Grant, Hilson, Lee.