The Red Lichties, who had not won a game so far this season and lost 3-0 at home to Ayr United the previous weekend, got off to a great start when Steven Milne capitalised on a mistake by Callum Morris.
The Pars player atoned for his error by heading in an equaliser and Shaun Byrne’s low shot put the Fifers 2-1 ahead in 41 minutes.
However, Gayfield summer signing Alan Cook scored a quickfire double to turn the game on its head just before the break.
Dunferrmline’s hopes of a fightback were dented when Chris Kane was sent off just six minutes into the second half.
Jefferies said: “We caused ourselves problems all afternoon and that has to stop. We are a target in this league and have to deal with that.”
Ayr United joined leaders Rangers on the six-point mark after beating Forfar 2-0 at Somerset Park. Craig Malcolm opened the scoring in the first half when he drove home his first goal for the club from ten yards. Michael Moffat sealed the win with a second-half penalty after veteran defender Darren Dods was red-carded for handling on the goal-line.
Stenhousemuir are the third team in the division to have maximum points after two games, and they did it the hard way by winning at Airdrie with only ten men.
Warriors kipper Ross McMillan was red-carded early in the second half for his second foul in quick succession on Jim Lister. But the visitors claimed all three points when Ross McNeill ran clear in the final seconds and kept his composure to fire home the winner.
Brechin City enjoyed a 2-0 win over East Fife at Glebe Park with substitute Ryan Donnelly heading the opener on 68 minutes and Alan Trouten running in on goal and sending a shot past former team-mate Michael Andrews to secure the win with seven minutes left.