Hearts always had the edge against Mark McGhee's Motherwell and substitute Saulius Mikoliunas fired a late winner just after David Clarkson's second equaliser.
Some slack defending had allowed both Michael Stewart and Audrius Ksanavicius to put Hearts in front during the first half.
Motherwell had a familiar look with only new outfield player Jim O'Brien limited to a late run-out, but they only briefly matched their performances from last season.
And McGhee, who rejected the chance to become Hearts boss in May, would no doubt have been angered by his side's defending.
Hearts were the better side and Laszlo would have been delighted with their spirit to bounce back less than two minutes after Clarkson's second-half strike.
With new signing David Obua injured the Hearts manager named a familiar line-up with Christos Karipidis handed the holding midfield role and Jamie Mole the main striking spot.
Laszlo's first match failed to tempt close to a full house but the Hearts fans who turned up were encouraged by their team's start.
Laryea Kingston shot a yard over following a strong run and Andrew Driver's cross just evaded Mole.
Bob Malcolm was booked for chopping down Driver as he burst down the left and new Motherwell skipper Stephen Craigan enjoyed a huge let-off in the ninth minute.
Last man Craigan lost possession to Ksanavicius but referee Iain Brines awarded a foul that did not seem apparent, although Graeme Smith saved the Lithuanian's shot as the whistle blew.
Ksanavicius was soon booked for diving after falling over Craigan's outstretched leg in the box.
Motherwell appeared to have steadied the ship but Stewart ran from deep to collect Driver's inside ball and drove home from 18 yards.
Smith kept Motherwell in the game when Driver's deflected effort from 22 yards looped over his head, the goalkeeper just managing to claw the ball and stop it on his line.
The save was immediately given greater value when Clarkson levelled in the 33rd minute. Stephen Hughes skipped past a defender and drove the ball across the goalmouth, where Clarkson bundled home.
Motherwell continued to improve and Clarkson looped a header over following Steven McGarry's cross.
But Ksanavicius put Hearts back in front in the 40th minute after the visitors were again exposed through the middle.
Headers from Mark Reynolds and Craigan only succeeded in putting Ksanavicius through on goal and the Lithuanian bravely stabbed the ball past the onrushing Smith.
Hughes almost levelled in the dying seconds of the half when he volleyed inches wide after a free-kick into the box was half-cleared.
Driver wasted an opportunity to put Motherwell under pressure after the break when he hesitated on the edge of the area after being sent clear by Ksanavicius, and eventually overhit his cross between two team-mates.
Hearts remained in control and Marius Zaliukas beat Smith to a high ball but saw his header drift away from goal, while Kingston was too high with two long-range efforts.
Marc Fitzpatrick replaced Malcolm as McGhee looked to add some drive to his three-man midfield but Zaliukas threatened again following a high ball with a powerful volley that was held by Smith.
Well enjoyed more possession but they struggled to create chances until Clarkson levelled out of the blue with 10 minutes remaining. The ball broke to the Scotland striker 20 yards out and he fired a powerful strike into the bottom corner.
However, Hearts quickly recovered from the shock and Mikoliunas struck 90 seconds later. Stewart played the Lithuanian in down the right and he strode forward before blasting the ball high into the net from 15 yards.
Motherwell came from behind to win and draw at Tynecastle last season but they could not fight back again despite some late pressure.
Chris Porter could not get enough power in his shot to beat Steve Banks from 12 yards following a set-piece and Stevie Hammell curled a free-kick wide, before Clarkson failed to connect properly with a last-minute volley.