City move above Clyde, now only five points ahead of bottom-placed Cowdenbeath, who beat Berwick Rangers 3-1 - their first win in eight games.
Annan Athletic leapfrogged visitors Elgin City after a 1-0 win.
Stirling Albion jumped above Montrose into fifth with a 3-1 win.
James Lister put Forfar ahead five minutes before half time, but former Celtic, Hibernian and Scotland striker Derek Riordan levelled and Lewis Allan secured the three points for Edinburgh.
Mark Whatley's goal was enough to secure victory for Arbroath against Clyde.
Annan moved up to third, David McKenna's 20th-minute penalty was the only goal of the game at home to Elgin as the sides swapped places in the table.
Robbie Buchanan, Brian Ross and Kriss Renton put Cowdenbeath in control in their first game under new manager Gary Locke before Greg Rutherford grabbed a late consolation for Berwick.
Stirling leapfrogged Montrose in the table courtesy of goals from Darren Smith, Ross Kavanagh and Connor McLaren.
Kerr Hay pulled one back for Montrose late on.
Arbroath moved within three points of Forfar Athletic at the top League Two thanks to a 1-0 win over Clyde as Edinburgh City beat the league leaders 2-1 at Station Park.