Coming into the contest with maximum points from their opening three Group F fixtures, Portugal appeared to be cruising towards a seventh successive World Cup finals.
The Seleção, however, were stunned early on against Hungary, with Attila Szalai heading in at the back post from Szoboszlai’s inswinging corner to give the visitors an eighth-minute lead.
Undeterred by that setback, Roberto Martínez’s side went in pursuit of a quickfire response, as Cristiano Ronaldo saw a low effort smartly saved by Balázs Tóth.
There was nothing the Magyars’ keeper could do soon after, though, with Portugal’s all-time leading scorer tapping home from Nélson Semedo’s inch-perfect cross to net his 142nd international goal.
Both teams continued to create chances as the first half progressed, but it was the hosts who completed their turnaround in stoppage time when Nuno Mendes’ delivery was clinically volleyed home by the irrepressible Ronaldo from six yards.
The Seleção came close to extending their lead at the start of the second period when Pedro Neto saw an angled strike thwarted by Tóth, while at the other end, Diogo Costa had to remain alert to deny Szoboszlai.
Keen to wrap up a seventh consecutive win on home soil, Portugal ramped up the pressure on the hour mark, as Rúben Dias powered a sublime long-range effort against the post before Bruno Fernandes struck the woodwork just a minute later.
Grateful for those reprieves, Hungary came within inches of an equaliser themselves, with Szalai directing a close-range header against the bar.
The Magyars continued to commit numbers forward in pursuit of a late leveller, and their pressure finally paid dividends in the first minute of stoppage time when Szoboszlai converted from Dániel Lukács’ cross at the back post.
That secured a crucial point for the visitors, who remain above the Republic of Ireland in Group F, while Portugal will have to wait until November to confirm their qualification for next summer’s finals.
Flashscore Man of the Match: Nuno Mendes (Portugal)