Robson's 78th minute rocket gave United their fourth win out of four against St Mirren this season and keeps alive their hopes of a top-six finish, while Saints remain second from bottom after their fifth straight defeat in 2007.
The Paisley club made the early running, but the first real chance fell to the visitors after 27 minutes when striker Noel Hunt narrowly failed to connect with Robson's cross from the left.
Two minutes later the same two players managed to link up but Hunt's diving header flashed wide.
Defender Christian Kalvenes soon set-up Hunt for a third crack at goal which Smith saved comfortably.
Saints defender Ian Maxwell then saw a scrambled effort hacked away inside the six-yard box, but United finished first half strongly with Robson heading over from close range and Craig Conway testing Chris Smith with a firm left-foot drive.
The second half also took time to catch fire and when it finally did United continued to threaten as David Robertson shot directly at Smith and Hunt found the side-netting.
Robson's wonder goal would have knocked the stuffing out of most teams, but substitute Stewart Kean and top-scorer John Sutton both missed chances to equalise.