The Scotland Under-21 midfielder atoned for his international disappointment in midweek by netting an 18-yard drive to end the Bairns' four-game losing run.
Michael Stewart appeared to have come to Hearts' rescue with a fine 71st-minute strike which levelled the scores at the Falkirk Stadium.
Earlier, former Tynecastle hero Neil McCann returned to haunt his old team by handing the Bairns a third-minute lead on his competitive debut.
But after Csaba Laszlo's charges had battled back into a hard-fought contest, Arfield had the last laugh to secure the club's first points to the relief of manager John Hughes.
As well as eventual man-of-the-match McCann, Falkirk were boosted by the return of Tam Scobbie, Michael Higdon and Burton O'Brien.
Hearts, meanwhile, were missing Andy Driver and David Obua, but Polish recruit Adrian Mrowiec, on loan from FBK Kaunas, made his debut alongside the recalled Saulius Mikoliunas.
McCann was keen to make an impression after leaving Gorgie in the summer - and the 34-year-old did so by giving his side an early lead.
Graham Barrett made a burst down the right and his cross was only partially cleared by Christophe Berra.
Injury-hit McCann, a 1998 Scottish Cup winner with Hearts, rifled an angled shot under the Slovakian Marian Kello.
Falkirk had started in lively fashion and came close to adding a second on eight minutes when Barrett's free-kick was only just deflected over for a corner.
Hearts sought a foothold in the contest and almost scored when Jamie Mole and Laryea Kingston linked up, with the latter striking a low shot towards the corner that was parried away by Robert Olejnik.
If Falkirk continued to look a threat on the break, Hearts were beginning to grow in confidence and almost conjured an equaliser on 21 minutes.
Mole did well to play in Mrowiec in the penalty area and with the Falkirk defence stretched, Jackie McNamara was on hand to clear the midfielder's effort off the line even if the ball appeared to be going wide.
After a blistering opening it was inevitable the match would lose some of its tempo, but McCann continued to drive Falkirk forward and his crosses from the left were proving a handful for Kello.
Kingston's tame header from an Eggert Jonsson cross was Hearts' reply before half-time.
Referee Steve Conroy became the target of criticism from home supporters for some dubious decisions, before he upset the visitors by cautioning Mikoliunas following a 50-50 challenge on Olejnik.
Hearts were straight on the offensive after the re-start, with Mole playing in the overlapping Mrowiec on the right and his dangerous cross was only just cut out by Olejnik as Stewart lurked.
Higdon, who had had a quiet game, responded with a neat curling drive straight at Kello.
Laszlo made an early double change on 52 minutes with Mikoliunas and Mole withdrawn for Christian Nade and Audrius Ksanavicius.
Hearts began to pin Falkirk back and only last-ditch clearances from Scobbie and Lee Bullen preserved the Bairns' lead.
O'Brien then threw his body in front of a fierce Ksanavicus drive with the Lithuanian demanding a penalty.
McCann was withdrawn to a standing ovation on 64 minutes, as fellow summer signing Steve Lovell came on.
But it was Hearts who got the goal their second-half efforts probably deserved on 71 minutes.
Under pressure, Barr cleared his lines but the ball fell at the feet of his Scotland colleague Stewart who fired a shot from 18 yards into the bottom right-hand corner.
As tackles flew in, Conroy was having a tough job keeping a grip of proceedings and delivered another spate of bookings in the second half.
Lovell had an excellent chance to restore the lead on 77 minutes, racing through on goal before cutting inside only for Marius Zaliukas to deflect his attempt wide. From the resultant corner, Bullen struck a shot into the ground that drifted past.
After a flurry of substitutions, the game looked set to peter out towards a draw but Falkirk had other ideas.
With a minute left, Lovell neatly played the ball back to Arfield - part of the Scotland Under-21 team who missed out on a European Championship play-off place - and he calmly placed a shot into the bottom left corner to spark much jubilation.
There was a late scare as Berra saw a downward header bounce up and hit the bar, but the Bairns held on.