Henk Veerman opened the scoring for Heerenveen after 29 minutes, but substitute Joey Sleegers equalised midway through the second half with a deflected shot.
NEC defender Rens van Eijden conceded a penalty five minutes from time and was sent off for a second bookable offence but Jones saved Mitchell Te Vrede's spot-kick to preserve a point and move NEC up to seventh.
Eredivisie leaders PSV Eindhoven coasted to an eighth straight win to open up a four-point advantage over Ajax.
First-half goals from Davy Propper and Gaston Pereiro gave PSV a comfortable 2-0 victory over Heracles Almelo, throwing down the gauntlet to Ajax, who play Excelsior later this weekend.
Heracles were hit for six by AZ last weekend and they must have feared the worst when Jetro Willems set up Propper for a composed third-minute finish.
But goalkeeper Bram Castro was in outstanding form to deny Propper and Marco van Ginkel and Heracles survived until the final minute of the first half.
Wout Weghorst was penalised for holding Jeffrey Bruma at a a corner and Pereiro dispatched the penalty with ease.
PSV failed to turn their dominance into further goals, but head coach Phillip Cocu will be delighted that his side were not taxed too much ahead of their UEFA Champions League clash with Atletico Madrid.
AZ leapfrogged Heracles into third place by beating Groningen 4-1 for a seventh straight victory.
Vincent Janssen struck for the 15th time in the league after 24 minutes and Ron Vlaar soon doubled the lead with his first AZ goal.
AZ should have added another from the penalty spot before half-time when Juninho Bacuna brought down Ridgeciano Haps, but Sergio Padt saved Markus Henriksen's poor spot-kick.
Haps did make it 3-0 from Dabney dos Santos's pass before Michael de Leeuw pulled one back from the spot after being felled by Joris van Overeem.
But Henriksen made amends for his penalty miss by grabbing his 13th goal of the season 19 minutes from time.
FC Twente beat bottom-placed Cambuur 3-0 for a fourth successive win.
Michael Peersman put through his own goal before Jerson Cabral claimed a second and Hakim Ziyech added a last-minute penalty.
