The visitors leapfrogged Caley Thistle and now have a point advantage and three games in hand over the Highlanders.
Buaben opened the scoring with a low shot from 10 yards on 74 minutes - within 60 seconds of coming on - and Robertson netted in the last minute from 18 yards with a low shot.
United manager Peter Houston made four changes to the side which drew 1-1 at bottom club Hamilton last time out. Danny Swanson, Morgaro Gomis, Barry Douglas and Stuart Armstrong were favoured ahead of Robertson, Buaben, Timothy Van der Meulen and Johnny Russell.
Influential attacking midfielder Jonny Hayes was a surprise inclusion for the hosts - the Irish winger returned for the first time since the 3-3 draw at St Mirren on February 12.
Chris Innes was the only other change for the Highlanders from the side which lost 2-0 at Hibernian on Saturday, with Eric Odhiambo and Russell Duncan dropped to the bench at Tulloch Caledonian Stadium.
The Highlanders started brightly with defender Grant Munro shooting just off target. Munro was in at left- back for the second consecutive game in a defence comprised of four centre-halves, with Ross Tokely in the other full-back slot.
At the opposite end, United had a back four of full-backs with Sean Dillon and Paul Dixon in the central positions.
Dangerman Jonny Hayes almost capitalised in the 11th minute when he powered down the wing past Barry Douglas before finding Richie Foran, whose free header brought an acrobatic diving save from Dusan Pernis.
Midfielder Stuart Duff was next to test Pernis with a 20-yard effort after being played in by Adam Rooney - but the goalkeeper made a low save.
Moments later Aaron Doran dragged his shot wide when he found himself room for an effort.
Irish winger Doran was then replaced by Nick Ross in the 27th minute after the midfielder pulled up when on another attack.
Tokely might have been lucky not to have been shown red moments later when he fouled Craig Conway on the edge of the area, after already being shown a yellow card earlier.
David Goodwillie produced an audacious flicked shot with his back to goal in 33 minutes when he met a Conway cross - but his effort was just off target.
On the counter-attack Jonny Hayes' cross-cum-shot just evaded fellow Irishmen Rooney and Richie Foran.
United's Danny Swanson and Inverness's Lee Cox had chances to break the deadlock before the interval but neither found the net.
The game started to become a midfield battle with chances at a premium for both sides following the interval.
Inverness goalkeeper Ryan Esson - making his 100th appearance - was forced into turning a low Goodwillie shot just past the post seconds after the restart.
Munro scuffed a shot wide when free at the edge of the area after being found by a Ross corner.
Esson was called upon again just before the hour when Swanson's stinging volley from 25 yards deflected off Innes en route to goal.
Substitute Buaben broke the deadlock for the visitors a minute after entering the fray.
The central midfielder sidefooted home after 74 minutes from 10 yards after being set up by Goodwillie.
Buaben might have scored even earlier - seconds after he replaced Inverness-born Stuart Armstrong the Ghanaian's 30-yard blast went just over.
Rooney could have equalised with just over 10 minutes to go but he headed a Foran cross just wide.
Chris Hogg cleared off the line to stop substitute Andis Shala doubling the lead after he rounded Esson.
But United were not to be denied a second with Robertson firing low into the net from 18 yards after being played in by Buaben.