Stevie Crawford’s side went into the game deep in relegation trouble while their visitors are enjoying a magnificent run of form at the opposite end of the division.
The two needed the three points for vastly different reasons and early on it looked as if the game would go with the form book.
Montrose started well and East Fife had to be on their toes to block a couple of Liam Callaghan deliveries.
But the Fifers soon grew into the game and created a few magnificent chances to open the scoring – chances they would later rue.
Kyle Connell was his usual busy self and his excellent turn and shot was blocked by the face of Andy Steeves.
The on-loan Kilmarnock striker was in the thick of things again when he picked up on a slack pass in the Montrose defence and scampered clear on Arron Lennox’s goal.
Connell got his shot away but found Lennox equal to it.
It’s doubtful that Montrose would have expected to be doing the volume of defending they were as East Fife kept up the pressure.
Lennox was being overworked but kept the scores level with a terrific save from Danny Denholm’s dipping volley.
East Fife went in at the break with their tails up but it was the visitors who started the second half much the better when Paul Watson’s drive whistled past Scott Gallacher’s post.
The home side were being increasingly penned deep inside their own half by Montrose and they made them pay when Blair Lyons finished from close range.
Losing another goal within minutes of shipping a first has been something of an unusual character trait for East Fife this season and it reared its unwelcome head again on Sunday.
Within barely seconds of Lyons opening the scoring the same man made it 2-0 when he got a touch to an Andy Steeves cross.
To their credit East Fife tried to force their way back into the game but their hopes were dented when they were reduced to 10 men when Connell saw a straight red.
Ross Campbell, deputising for the absent Stewart Petrie, said his side were well worth their win for their second 45 showing in particular.
He said: “I’m really pleased for them because they’re brilliant, a really good group of boys who enjoy what we do and that comes through.
“But they’re paid to perform and managed to dig it out at a hard place to come.”
Simpson has joined the club on a short six-month deal until the opening of the summer transfer window.
Having played for Tooting & Mitcham United, Westfield and Farnborough FC, the 25-year-old has been closely followed by a number of lower league clubs north of the border since becoming a free agent last October.
Manager Petrie said: “Eli is an exciting prospect.
"He has impressed in training and brings a different dimension to our attacking options.”