Hearts took the lead in the fifth minute when Lee Wallace's cross caught out Robert Olejnik at the near post and sailed into the net.
Dawid Kucharski scored an own goal in first-half injury time to bring the visitors level but Suso Santana and Black struck after the break. Falkirk substitute Pedro Moutinho notched a consolation goal with seven minutes left.
The new Hearts management team of Jim Jefferies, Billy Brown and Gary Locke were granted a standing ovation from the supporters on their return to Tynecastle as they were paraded prior to kick-off.
And the Hearts fans were on their feet again after five minutes to celebrate Wallace's bizarre opener.
Picking up a short pass from Ryan Stevenson, the left-back's cross-cum-shot caught Olejnik by surprise at his near post as the goalkeeper was unable to claw the ball clear.
Buoyed by the early strike, the hosts went looking for a second but David Obua was unable to make a powerful connection with Santana's cross.
Bairns defender Brian McLean needed medical assistance after picking up a head knock in the challenge with Obua but was able to continue.
Eggert Jonsson then picked out the towering Ugandan with a near-side delivery but he failed to find the target with his header.
Obua did have the ball in the net in the 22nd minute but Arvydas Novikovas was adjudged to have run the ball out of play at the byline before crossing.
Hearts enjoyed the lion's share of territorial possession but were struggling to find gaps in a resolute Falkirk defence.
A hopeful ball into the Hearts box, however, caused problems as goalkeeper Marian Kello was forced to come from his line to block Carl Finnigan's shot at a tight angle.
With Kello out of his goal, Finnigan lofted a pass back into the area but Black headed clear.
A defensive error from Wallace's cross into the Falkirk box gave Santana a chance to shoot but his left-footed effort was well blocked.
Ten minutes before half-time, Stevenson fired a low half-volley goalwards that was saved by Olejnik at the second attempt.
Falkirk defender Tam Scobbie then did well to header clear from under his own crossbar as Novikovas attempted to find Obua.
The Bairns levelled in first-half injury time when defender Kucharski scored an own goal.
Marc Twaddle fired a low volley across goal from Finnigan's flick-on and the Pole could not get out of the way as he diverted the ball into the net.
New Falkirk manager Pressley made his intentions clear at half-time by going with two in attack.
Towering marksman Enoch Showunmi came on for winger Jack Compton.
And Falkirk winger Ryan Flynn missed a great chance in the 55th minute. The visitors broke at pace from a Hearts corner and Showunmi was able to squeeze a pass to Flynn under pressure from Kucharski but the former Liverpool trainee volleyed over from six yards.
Hearts breathed a sigh of relief on the hour mark when Burton O'Brien swung a left-footed free-kick over the wall from 25 yards and missed the target by inches.
Despite Falkirk's pressure, Hearts added a second a minute later through Santana. Novikovas' deep cross from the left flank was not dealt with by Olejnik and the Spaniard cracked a shot into the net from six yards.
Black gave Hearts a two-goal cushion with a 25-yard thunderbolt that flew past Olejnik in the 67th minute. The diminutive playmaker edged past McLean and unleashed an unstoppable left-footed drive.
Hearts were now brimming with confidence as they sprayed passes around with authority. Santana picked out the unmarked Gary Glen at the corner of the box with a cross-field pass but the striker blasted his shot over.
Falkirk responded by throwing on a third striker in the shape of Moutinho, with Colin Healy making way.
And Moutinho set up a tense finish after finding the net for the Bairns seven minutes from time. Wriggling free in a congested penalty box, the substitute drilled a shot high into the net from close range.
Falkirk won a series of free-kicks in Hearts' half but they failed to make any of them count.
Source: Team Talk