Danny Coulson scored twice for the hosts with Fraser Shields grabbing their third. Chris Fairhurst and Will Richmond replied.
Rawcliffe ’keeper Leon Finney was the hero of the day, saving a penalty when the home side led 2-1.
Paul Scaife (2) and Kieron Harris gave Haxby a 3-1 lead at the break, with Stuart Dickinson notching for Heslington.
Heslington tried to mount a second-half comeback but could only force an own goal to reduce the deficit as they paid for a one-sided first half.
Danny Hall (2), Jamie Husband and Dom Harris combined to give Fulford a 4-1 win at Thorpe.
In division three, Stamford Bridge scored a 4-0 home win over third-placed York Acorn thanks to strikes from John Cavanagh, Oliver Lee and Sheridan Fletcher, plus an own goal.
Bishop Wilton hit five past Tadcaster Town without reply. Rob Eeles, Charlie Bond (2), Jason Nattrass and Alex Nattrass got their goals.
Huby rounded off their campaign with a 3-1 home defeat to Civil Service. Chris Phillips bagged for Huby but they were outdone due to finishes from Matt Deighton, Dec Richardson and Rob Orr.
Rufforth hit Crayke for six, with the travelling side having no answer. Lee Bartlett fired a hat-trick, with Mark Powell (2) and Joe Bootland also bagging.
• Don’t miss The Press tomorrow for more reports from the York Minster Engineering League.