Top scorer Alan Armstrong netted one and set up Che Adams, Ryan Fraser and Sekou Mara as Saints briefly leapt into the top two for the first time since the opening day and closed the gap to table-toppers Leicester to ten points.
Saints are now unbeaten in 19 league games and 20 in all competitions, which is their best run since becoming a Football League club in 1920.
The club's all-time record of 24 in 1896 and 1897 came when they were known as Southampton St Mary's and had yet to move to the Dell.
Martin said: "We are on an unbeaten run where I'm immensely proud of the players. It is incredible what they have achieved and we have to keep it going as long as possible.
"It has never been a conscious focus for us, but I want them to go and make some history next week.
"I want them to be remembered for that. I want them to do it and it has been an incredible achievement.
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