The victory puts Twente second on 43 points, one behind Ajax, but ahead of Vitesse Arnhem, who lost at home to AZ Alkmaar on Tuesday.
Tadic netted his ninth goal of the season when his left-footed effort in the 72nd minute took a wicked deflection to beat Heerenveen goalkeeper Kristoffer Nordfeldt.
Borven added the second on the stroke of fulltime.
Jeffrey Bruma and Jurgen Locadia scored as PSV Eindhoven came back after conceding an early goal to win 2-1 away at SC Cambuur.
PSV stay seventh, 12 points behind the leaders after a topsy-turvy season for their young side which has an average age of 21.8 years.
NEC Nijmegen remain second from bottom after being held 1-1 at home by NAC Breda, but RKC Waalwijk moved up to 14th after securing a point with a 2-2 draw at Go Ahead Eagles.
Ajax can go four points clear if they win at home to Groningen on Thursday.