Twente, who needed extra time to qualify for the Europa League against Bursaspor on Thursday, looked sluggish and lacked creativity.
However, when Ismo Vorstermans fouled teenage striker Mirco Born in the 90th minute, Fer stepped up to score from the spot.
Twente head the table with 12 points, two ahead of Vitesse Arnhem, who brought Feyenoord's 11-match unbeaten run after beating the Rotterdam club 1-0 when striker Wilfried Bony scored with a back heel late in the game.
PSV Eindhoven moved up to third after seeing off 10-men AZ Alkmaar 5-1.
The visitors had Etienne Reijnen sent off for two yellows after just eight minutes and PSV went ahead shortly afterwards when Tim Matavz scored from close range.
Adam Maher levelled just before the half-hour mark with a fine effort from distance, but Mark van Bommel, Marcelo, Matavz again and Atiba Hutchinson sealed a comfortable win for the home side.
Ajax slipped to fourth after they could only draw 2-2 at Marco van Basten's Heerenveen.
South African international Thulani Serero put the visitors ahead after 13 minutes, but Heerenveen looked strong, with Alfred Finnbogason getting a deserved equaliser shortly after his team-mate Filip Djuricic missed a penalty.
Finnbogason then put the home side ahead just before half-time, only for Serero, who was later red-carded for a wild tackle, to equalise shortly after the break.
