Depleted even before kick-off by injuries to a key defender, Takis Fyssas, and a first-choice striker, Roman Bednar, George Burley's side then suffered a calamity when Craig Gordon, their Scotland goalkeeper, was sent off after 25 minutes for hauling down Darryl Duffy, who converted the subsequent penalty.
Worse was to come when Julien Brellier - the closest Hearts have to a Claude Makelele figure in as much as he is French, plays a holding/distribution role and at his best can switch play from defence to attack with one pass - went off injured before half-time. He suffered a suspected broken rib and was, according to Burley, "passing a lot of blood".
Then, midway through the second half, Duffy rifled a shot at Gordon's replacement, Steve Banks, who could only parry it at Pressley, off whom it rebounded back into his own net.
Yet somehow, despite playing with 10 men for more than an hour against spirited opponents - Duffy and the creative Russell Latapy exemplified Falkirk's approach - Hearts rallied to secure the draw.
Pressley made it 2-1 after meeting a Rudi Skacel free-kick at the far post. Then the Scotland centre-half got his second/third goal in the final minute after an attempt by Skacel fell into his path.
Cue mayhem, and an attempted pitch invasion by delirious Hearts fans, who were quickly calmed by a few local police. There were some tongue-in-cheek suggestions that the coppers should be investigating the mugging that had just taken place on the pitch. Yet Hearts' spirit, if only in a frantic final 15 minutes, really swung it.
They will need such nerve in their next match, against Celtic, who scored five at Livingston on Saturday, just as Rangers were helping to reassert the Old Firm threat by scoring five against Dunfermline.
"For our character, spirit, energy, desire, I thought we deserved the point," Burley said.
Goals: Duffy pen (27) 1-0; Pressley og (67) 2-0; Pressley (72) 2-1; Pressley (90) 2-2.
Falkirk (4-4-2): Glennon; Lawrie, Rodrigues, Ireland, Milne; Thomson, Lima, Latapy, O'Donnell (O'Neil, 69); Gow (Moutinho, 86), Duffy (McBreen, 83). Substitutes not used: Hill (gk), McPherson, Scally, McStay.
Heart of Midlothian (4-1-3-2): Gordon; Neilson, Pressley, Webster, McAllister; Brellier (Wallace, 38); Camazzola (Cesnauskis, 77), Hartley, Skacel; Jankauskas, Pospisil (Banks, 25). Substitutes not used: Simmons, Mikoliunas, Elliot, Tall.
Referee: I Brines.
Booked: Falkirk Rodrigues, Lima; Hearts Jankauskas.
Sent off: Hearts Gordon (25).
Man of the match: Duffy.
Attendance: 6,342.Reuse content