A 1-0 win means that Town will have home advantage for their play-off match whether they finish third or second, writes Tom Feaheny.
The victory at Southport means that Town are on a good run going into the crucial last week.
“This is an important win that helps with our end of season planning and preparations,” Wilkin told the club's website,
“There weren’t too many chances but we scored a good goal.
"Danny Lewis earlier made a very good save so it’s a pleasing three points for us to get back to winning ways.”
Brackley have two home games to go before the play-offs get underway as they face Chorley and York City in the next six days.