Ronan Doherty teed up a great chance early in the game, but his pass couldn't be steered home by a red shirt.
Larne became more frustrated as the half progressed, but they were awarded a free-kick on 22 minutes and Ryan produced a great finish from 30- yards that had stopper Declan Dunne clutching at thin air.
Tiernan Kelly came close to an equaliser when he volleyed wide at the back post before Ryan clipped the crossbar with a header at the other end.
The Scottish striker did get his chance for a second just before half-time when Gael Bigirimana brought down Sean Graham in the box.
Ryan then calmly rolled the ball into the bottom corner to double his tally and the Larne lead at the break.
The second half never really burst into life with Dungannon unable to get back into the game, while Larne struggled to extend their advantage.
Kealan Dillon tried his luck from long range, but Rohan Ferguson made a simple save before Dunne, at the other end, denied a Matt Ridley header from a corner.
Substitute Paul O'Neill then struck the foot of the post from a corner, but it looked as though that would be a final chance as a second half low on quality chances meandered to a close.
However, in the 89th minute, Mitchell hauled the visitors back into the game out of nothing when he latched onto a flick on from James Knowles and lashed home a stunning volley from a narrow angle.
That brought about a late push from the away side with Ferguson forced into a couple of saves as the men in blue packed into the penalty area.
Ultimately, though, Larne held on for what could be a crucial three points at the top of the table.