Marco van Basten's side consolidated sixth place in the table in their chase for a UEFA Europa League qualification berth.
With the Eredivisie's packed nature - much of the league remains in with a chance of making the Europa Leauge play-offs - Finnbogason's 22nd league goal of the season could prove a crucial one.
They had to come from behind to seal the points after Oussama Tannane gave the hosts a 26th-minute lead, curling a delightful free-kick into the top right-hand corner from 30 yards beyond a despairing dive from Kristoffer Nordfeldt.
Ten minutes later however, Heracles surrendered their advantage as Marten de Roon nodded home Hakim Ziyech's right-wing set-piece from six yards.
Four minutes into the second period, Finnbogason struck, tapping home the rebound after Remko Pasveer had parried Rajiv van La Parra's initial effort.
The hosts responded well, Nordfeldt reacting smartly to tip Tannane's header behind before the resulting corner landed on top of the crossbar and bounced away to safety.
Heerenveen survived a late scare, Mark Uth flashing a volley narrowly wide in stoppage time as Heracles' winless run extended to four matches.
