Nicky Clark curled in a 25-yard free-kick for the home side in the 18th minute before United's number two keeper Deniz Mehmet, making a rare appearance, made several good saves to keep a sturdy Livi side out.
However, the Taysiders' resistance was broken in the 53rd minute when defender Jon Guthrie clipped a shot in from eight yards.
Gary Holt's side kept on top for most of the rest of the second half and in the 90th minute, the United defence found themselves outnumbered and Forrest was able to tap in a pass from substitute Matej Poplatnik.
The win took Livingston above Dundee United and into sixth place in the table.
There was some surprise when it was revealed that United goalkeeper Benjamin Siegrist was absent from the squad but manager Micky Mellon said pre-match he had a strain as Mehmet made his first appearance in over a year.
Defender Mark Connolly took over from Mark Reynolds who dropped to the bench, also with a slight strain.
Holt stuck with the same side which started in the win over St Johnstone last weekend and in a frenetic start to the match, his charges made as many sloppy errors as the home side.
After some time allowed by referee John Beaton for the Livingston player to get treatment, Clark stepped up and curled the ball round the Livi wall and in at Robby McCrorie's left-hand post for his third goal of the season.
Holt's side hit back with force.
Mehmet made an impressive double save, first from Forrest's curler from distance and then tipping Scott Robinson's shot on the follow-up over the bar with the corner defended.
Mehmet again thwarted Robinson in the 38th minute when the United defence had been opened up, pushing the forward's drive from 12 yards past the post and again the corner came to nothing.
Just before the break Mehmet blocked yet another effort, this time an angled drive from Scott Tiffoney who had breached the back line.
The Lions kept pushing after the break, racking up the corners and eventually the pressure paid off when Guthrie, still in the box from a previous set-piece, swept in a cross from captain Marvin Bartley.
United remained subdued as Livingston kept piling forward with the home side straining to keep them at bay.
Holt was yellow-carded by Beaton for complaining about an offside decision and it looked like a draw was on the cards.
However, there was to be a sting and it came when Robinson robbed Connolly and as Livingston broke in numbers, Pittman played in Poplatnik, who squared to Forrest to tap into an empty net with no time for United to respond.