Matt Crooks gave bottom-of-the-table Boro hope with a 55th-minute reply but, including last season’s two-legged play-off final defeat to Coventry, the Teessiders have now gone 11 games without a league win, equalling the club’s longest sequence outside the top flight since January 1925.
The game kicked off amid a mood of celebration as the hosts commemorated the landmark occasion by welcoming a series of club legends onto the pitch.
Among them were Premier League-winning defender Colin Hendry, former PFA chief executive Gordon Taylor and 89-year-old Bryan Douglas, who played for England at the 1958 and 1962 World Cup finals.
Rovers appeared buoyed by that reception and Tyrhys Dolan should have opened the scoring less than two minutes in, but he headed over an empty goal after Callum Brittain’s pinpoint right-wing cross had taken Boro goalkeeper Seny Dieng out of the equation.
The Senegal international was in the right position to parry away from Lewis Travis shortly afterwards.
Jonny Howson went on to fire too high with the visitors’ first attempt of the afternoon at the midway point of the half, before Szmodics fittingly grabbed the game’s opener just after fans had begun clapping on the half-hour mark in memory of PA announcer Matt Sillitoe, who tragically passed away last month at the age of 30.
After Sam Gallagher stepped over a forward pass by Hayden Carter, the ex-Peterborough midfielder swept a strike inside Dieng’s right-hand post from the edge of the box.
Boro rallied, with Marcus Forss forcing a smart near-post save from Aynsley Pears, while Emmanuel Latte Lath should have done better with two great headed chances from Howson dead-ball deliveries, directing the first wastefully wide and the second tamely at the home keeper.
An unchallenged Gallagher also missed the target for Rovers with another aerial opportunity from six yards on the stroke of half-time.
Dieng then had to be alert to deny Dolan just 25 seconds after the restart following a Szmodics right-wing raid, but the latter extended the lead in the 49th minute.
Receiving the ball from Ryan Hedges, Szmodics drilled a 20-yard effort that Dieng could only help into the top corner.
Boro refused to surrender, though, with Crooks cleverly flicking in from six yards from Forss’ cross to reduce the deficit.
After Dieng made a double save to deny Adam Wharton and Dolan, Boro then missed three great chances to level, with Latte Lath ballooning over, Forss prodding wide and Darragh Lenihan heading too high.
As the match continued to swing from end to end, Dieng displayed more sharp reflexes to deny Hedges twice and make a one-on-one stop to prevent Szmodics from claiming the match ball.
The profligate Latte Lath, meanwhile, burst clear on goal at the death, only for his heavy touch to gift Pears the chance to snatch the ball off his feet.