Fort rallied after surrendering an early 2-0 lead to win the penalty shootout and set up a home North Cup second found tie against North Caledonian League club Invergordon.
Fort William manager Ally Ewen said: “We deserved the victory, I was disappointed we let the 2-0 lead slip but we got the result we deserved.
“I was impressed at how well we took our penalties so we can now look forward to the next round.” Disappointed Lossie attacker Martin Charlesworth, who grabbed his side’s opener, said: “We found ourselves 2-0 down after just 18 minutes but managed to get back to 2-2 by the half hour.
“We thought we had gone ahead when Ally Bellingham’s corner kick hit the post, the ball went straight back to him, he crossed and I headed home – we turned away to celebrate, the referee signalled a goal and Fort were about to re-start when the referee spotted the assistant with his flag up, so the goal was disallowed.”
An early Scott Davidson double took his tally to an impressive 25 for the season, but a 24th minute Charlesworth goal and a superb 18-yard Liam Archibald drive on the half hour levelled it at 2-2.
Michael Corbett put Fort ahead in the 73rd minute but six minutes later Ross Duncan made it 3-3 from the penalty spot after Ryan Farquhar had been brought down in the box.
The game went straight to penalties and Fort held their nerve to record victory.