Rodriguez's goals were his first domestically in almost 18 months, having only recently returned from a lengthy lay-off with a ruptured anterior cruciate ligament
He netted for the first time since his comeback against Danish outfit Midtjylland in the Europa League last month but his efforts on Wednesday night were his first strikes in English competition since a Premier League double against Newcastle on March 29, 2014.
The 26-year-old's brace, his second from the penalty spot, came either side of Mane's double while Long grabbed his two later in the second half - making it the heaviest defeat in MK Dons' short history
They had actually started confidently, knocking the ball about well
But a mis-placed pass was pounced on by Rodriguez, who punished the Championship side in the fifth minute
Rodriguez collected the ball near the halfway line and raced clear down the left before cutting inside and curling a lovely right-foot finish beyond David Martin and in off the far post
Cedric Soares and Oriol Romeu went close as Southampton sensed a swift second
It arrived after 10 minutes when Mane went past his man down the right side of the box and clipped his finish over the advancing Martin.
The hosts struggled to get a foothold in the game
Their only shots on target in the first half came from Carl Baker and Daniel Powell but both were easily fielded by goalkeeper Maarten Stekelenburg.
Southampton looked dangerous every time they attacked and they scored again in the 25th minute when Long crossed for Mane, who cut back on to his left foot and curled his shot into the bottom corner from near the penalty spot.
Summer signing Juanmi was denied a goal on his first start as Martin helped his shot over the crossbar and the Premier League team went into half-time 3-0 ahead.
The Dons began the second half in the worst possible way when McFadzean brought down Long, allowing Rodriguez to score from the spot after 48 minutes.
Virgil van Dijk's powerful free-kick clipped the top of the crossbar shortly afterwards before Long got the goal his performance probably deserved - but it had a large stroke of luck about it
McFadzean cleared Juanmi's cross against the Republic of Ireland striker and the ball bounced into the net
There was nothing fortunate about his second goal in the 75th minute when he latched on to Steven Davis' through-ball and finished from the edge of the area
Rodriguez thought he had completed his hat-trick with nine minutes remaining but he was denied by an offside flag
Source : PA