After playing out a goalless first half, the two sides were forced off in the opening stages of the second period due to a small fire behind the goal.
Striker Igor Paixao wasted little time in putting Feyenoord in front once the players returned to the pitch following a lengthy stoppage.
Feyenoord's task was made tougher when Yankuba Minteh was sent off in the 72nd minute, but Arne Slot's side ultimately stood firm to win the cup for the first time in six years and deny NEC their first major trophy.
Feyenoord move ahead following lengthy delay
NEC were making their fifth appearance in a cup final and their first since finishing runners-up to Roda JC in 1999-00.
Motivated by the chance to win the cup for the first time, NEC went agonisingly close to opening the scoring in the eighth minute, with Youri Baas' downward header forcing Timon Wellenreuther into a fine stop.
Following a cagey period of play, Rogier Meijer's charges thought that they had found the all-important breakthrough in the 29th minute.
Tjaronn Chery fired the ball in off the near post, only to see his strike ruled out for an offside infringement, ensuring that the final remained goalless at the break.
The second half was only 10 minutes old before play was halted after a banner in the stands caught fire behind the goal, leading to a lengthy break as the appropriate personnel dealt with the issue.
Feyenoord quickly hit their straps once play resumed, taking the lead through Paixao just before the contest had reached the hour mark.
Paixao latched onto Santiago Gimenez's pass to squeeze his sweeping effort past former Barcelona goalkeeper Jasper Cillessen, who could only push the ball against the post and watch it bounce back into the net.
Minteh sees red
For a brief moment, defender Lutsharel Geertruida thought that he had strengthened Feyenoord's lead, before his close-range effort was chalked off due to an offside call.
From nearly doubling their advantage, Feyenoord quickly found themselves down to 10 men after Minteh was given his marching orders for two bookable offences.
NEC attempted to make the most of their numerical advantage, with Roberto Gonzalez heading straight at Wellenreuther before Philipp Sandler's long-range drive drew a strong diving stop from the Feyenoord goalkeeper.
Although they threw caution to the wind, NEC's quest for an equaliser ultimately proved fruitless as their fifth cup final appearance produced yet another defeat.
While NEC's wait for a major trophy will go on, Slot will celebrate his second piece of silverware as Feyenoord boss after previously leading the club to the Eredivisie title last season.