There was just a minute left of extra time when substitute Nicky Maynard cheekily clipped the ball past Forest Green keeper Luke McGee and rolled it into the empty net, leaving County 5-4 aggregate winners despite losing 4-3 on the night.
They will face Morecambe at Wembley on Monday, May 31 with a place in League One on the line.
Newport led 2-0 from Tuesday's first leg but Rovers made the perfect start on Sunday, wiping out the deficit inside eight minutes.
The opener came when Nicky Cadden's free-kick on seven minutes picked out Ebou Adams 10 yards out and he guided his header beyond keeper Tom King.
Less than a minute later it was Baily Cargill's inch-perfect cross that did the damage with Aaron Collins - whose brother Lewis scored Newport's second on Tuesday after Matty Dolan's stunning opener - providing the finish with a first-time shot that squeezed past the Exiles keeper.
Having suffered a nightmare opening, the visitors eased their way back into the game and created a number of chances themselves.
Ryan Haynes had a long-range effort blocked, with Anthony Hartigan putting another chance over the target from distance. Then on the half-hour, a cross from Aaron Lewis picked out Mickey Demetriou but the defender failed to keep his header on target.
Both sides had penalty claims waved away by referee Martin Cox late in the half. Lewis Collins appeared to be shoved over for the visitors while at the other end, Aaron Collins went to ground as he looked to round the keeper which earned him a booking for simulation.
Aaron Collins was proving a handful for the Newport defence and he almost made it 3-0 in added time only for his shot to be pushed onto the bar by keeper King.
Forest Green did take the overall lead soon after the restart. Exiles boss Michael Flynn made a double change at the break with the introduction of midfielder Joss Labadie and striker Ryan Taylor, but it was a defensive error that cost them as Cadden's 30-yard free-kick eluded everyone and ended up in the back of the net.
More changes followed for the visitors, including the arrival of 42-year-old Kevin Ellison, and it was the veteran who levelled the tie on aggregate with a stunning 25-yard effort that went in off the underside of the bar on 70 minutes. Ellison will surely relish the chance to lock horns with his former club Morecambe at Wembley, having raucously celebrated his goal in March's regular-season meeting.
With both sides looking for a winner, Cargill was inches away for Rovers with a header that was cleared off the line but on 76 minutes, Labadie scored Newport's second on the night when he turned in Haynes' cross from the left flank.
But the tie was forced into extra time when Forest Green's Jamille Matt, playing his first game in nearly two months after injury, steered an Odin Bailey cross home from six yards.
Maynard missed a chance to score early in extra time but made amends with his last-gasp effort to wrap up a Wembley appearance.