Jamie Hamill converted a penalty on his competitive debut as Hearts earned a first-leg draw in their Europa League qualifier in Hungary.
Against the run of play, Istvan Sipeki gave Paksi the lead with a cool lobbed finish on 32 minutes.
But Hamill levelled in first-half injury time after striker John Sutton was impeded from a free kick.
The Hearts defence was seldom troubled as the visitors enjoyed long spells of comfortable possession.
Hamill and Sutton both had chances to grab a win for Jim Jefferies' side but Norbert Csernyanszki saved from the former Kilmarnock midfielder and the lone striker sent the awkward rebound over the crossbar.
Hearts started well at Videoton's Sostoi Stadium, with David Obua, Hamill and David Templeton trying their luck with shots from distance.
Obua started even though the Ugandan had a stressful trip after making a late dash to London to renew his passport before encountering visa complications at immigration in Budapest airport.
With fewer than 3,000 fans watching, the match was played at a leisurely pace throughout, Hearts knocking the ball around with assurance.
The Paksi goal came completely out of the blue when Laszlo Bartha's initial effort from outside the penalty box was blocked by Eggert Jonsson and Sipeki cleverly struck the bouncing ball over the stranded Marian Kello.
Buoyed by the goal, the Hungarians began to commit more players in attack but the teams were level on the stroke of half time.
Sutton was hauled to the ground by Tibor Heffler as he tried to reach Danny Grainger's free-kick and Hamill coolly lifted his spot-kick high into the net.
With both sides playing one up front, the cautious nature of play continued in the second half.
Following the opportunities for Hamill and Sutton, Paksi briefly threatened when a header from Tamas Sifter was pushed on to a post by Kello and a free kick from Gabor Vayer whistled wide.
But Paksi failed to gain any momentum and, with an away goal, Hearts will go into next week's second leg full of confidence.
However, Jefferies will be fully aware of the fact that the Hungarians progressed to this stage with a 3-0 win at Tromso after a 1-1 draw at home.