With just a minute left, substitute Steve Lovell pulled the ball back into the midfield player's path and he guided a precise shot beyond Marian Kello.
It gave Falkirk their first league victory of the season and, if a draw was perhaps a more accurate reflection, John Hughes was not complaining.
Neil McCann, making his first start for the club, took less than three minutes to make his mark. Graham Barrett's cross broke to him off Christophe Berra and he delivered an accurate finish beyond Kello.
It was the winger's first SPL goal since February 2003 when he netted for Rangers against Dunfermline.
Hearts did not look comfortable with Falkirk's eager front players running at them and Berra was forced to concede a free-kick just outside the penalty area.
Michael Higdon powered the free-kick towards goal but the wall did enough to deflect the ball for a corner.
It was a lively opening and Laryea Kingston tested Robert Olejnik with a low 20-yard shot which the goalkeeper did well to divert for a corner.
At the other end, Arfield was given far too much space as he homed in on goal but his 25-yard shot was yards too high.
Adam Mrowiec worked himself an opening midway through the first half after combining with Jamie Mole but Jackie McNamara thumped his effort clear even though it looked to be drifting wide.
Saulius Mikoliunas then had acres of space on the left with Falkirk caught short at the back but he dallied in possession and the chance was lost.
Hearts were allowing the Falkirk defence no time on the ball as they hounded them at every opportunity and it certainly unsettled the home team.
But, for all their work, they rarely managed to get in behind the Falkirk defence in the first half and Olejnik was not over-involved.
A sloppy pass from Tom Scobbie gave Hearts another opportunity but Lee Bullen was alert to the danger and managed to get the final touch before Mole could take advantage.
Hearts stepped it up in the second half and Darren Barr did brilliantly to get his head to a cross from Mrowiec with Mole waiting in the middle.
Michael Stewart was taking on a more influential role and he grabbed the game by the scruff of its neck to try and salvage something for Hearts.
It was fitting that he should supply the equaliser when he pounced on a headed clearance from Barr to rifle a low 20-yard shot beyond Olejnik.
Falkirk tried to hit back and substitute Lovell took on the Hearts defence single-handedly but his shot was deflected narrowly wide with Kello exposed.
In a frantic finish, Arfield nabbed the winner but Hearts almost snatched a draw in stoppage time when Berra's header from Kingston's corner struck the crossbar.