East Kilbride were 3-1 winners at their K Park home, Declan Hughes, who scored a brace, and Ross McNeil earning spots in the record books with the goals.
The part-timers have surpassed the previous benchmark set by a legendary Ajax team of the 1970's, which contained greats like Johan Cruyff, Johan Neeskens and Johnny Rep that won 26 games in a row between October 3 1971 and March 29 1972.
According to the Guinness World Records, that Ajax team scored 78 goals and conceded just 18 as they won 19 Eredivisie matches, four European Cup games and three Dutch Cup outings.
Following East Kilbride's historic victory there was a video message to the club from former Ajax and Manchester United keeper Edwin van der Sar, who congratulated the club on their achievement.
Ajax also sent a van filled with champagne and 27 crates of Dutch beer onto the pitch which the players distributed to fans.
East Kilbride's run began last March, with a 3-2 success at Whitehill Welfare. They have since won 15 league games in sequence, including their first 12 of the 2016-17 season to open up a commanding 13-point advantage over Spartans.
Winning the league would send East Kilbride - who have never played in Scotland's league system - to a play-off against the winners of the Highland League for a place in League Two.
