Soriano came off the bench to open the scoring midway through the second half. The goal came out of the blue as Nenad Krsticic had been given a straight red card just 18 seconds after the interval.
Despite being in charge for only four days and playing the entire second half a man down, Mihajlovic's side snapped a three game losing streak and leave Lazio still searching for a first away win of the season. Vladimir Petkovic remains under pressure as the point fails to mask another poor performance from his below-par team.
Both sides came into the game without their first choice strikers. Eder was suspended for the hosts, while Miroslav Klose was nursing a shoulder injury for the visitors. Michael Ciani returned to the Lazio backline following a suspension.
Sampdoria gambled on a 4-2-3-1 system. Lazio experimented with a 3-4-3, dropping Hernanes and Lucas Biglia to the bench.
A flock of pigeons settled in the Lazio half as both sides struggled to adapt to a heavy pitch. The home side asked all the early questions. Pedro Obiang dragged a shot wide from the edge of the area and an outstretched Pawel Wszolek just missed getting on the end of Nicola Pozzi's flick-on.
Federico Marchetti easily gathered a long range effort from Manolo Gabbiadini on the half hour. Samp then produced the best chance of the half five minutes later. Pozzi shaped to shoot in the area, but Abdoulay Konko put himself in the way to block the goalbound effort.
Lazio fashioned their first effort on goal three minutes before the break, as Sergio Floccari drilled a low shot from distance into Da Costa's gloves. The lively Keita Balde Diao released Konko in space, but the defender wasted a golden chance to cross in the box by sending the ball into Row Z.
Marchetti got across to save Gabbiadini's direct free kick as Mihajlovic went into the half time team talk the happier of the two managers.
Whatever Mihajlovic said during the interval went out of the window just 18 seconds after the restart when Krsticic was given a straight red card. Already on a caution from the first half, Krsticic stamped on Ledesma in full view of the referee who had no hesitations in dismissing the player.
Lazio introduced Brayan Perea and were more adventurous going forward. Konko sent a diving header wide, before Perea struck the post after a Senad Lulic pass made it through the Samp defence. There was a hint of offside on the attacker, but the flag stayed down.
Sampdoria went ahead against the run of play midway through the second half. Marchetti saved Gabbiadini's initial shot from distance. Soriano chased the rebound as the ball looped into the air, Marchetti tipped it against the crossbar, but was powerless to stop the substitute from nodding in.
A desperate Petkovic threw on Hernanes and Ederson as a last roll of the dice. Even with the numerical advantage, Lazio still looked disjointed and sloppy, struggling to create much of note.
Ederson pulled a shot wide from the edge of the box and Sampdoria made defensive adjustments to see out the game. However, Lazio pulled a proverbial rabbit out of the hat with the game's final chance. Cana latched onto a long ball forward, cutting inside the box and placing his shot past Da Costa inside the near post. Lazio's jubilant players celebrated with the Albanian, leaving Mihajlovic with a wry smile on his face in the Sampdoria dugout.
Sampdoria: Da Costa; De Silvestri, Mustafi, Palombo, Costa; Obiang, Palombo; (Maresca 90+3) Gabbiadini, Krsticic, Wszolek; (Soriano 59) Pozzi (Petagna 80)
Lazio: Marchetti; Radu, Cana, Ciani; Lulic, Onazi, Ledesma, (Hernanes 68) Konko; Candreva, (Ederson 70) Floccari, Keita (Perea 57)
Goals: Soriano 67 (S) Cana 90 + 4 (L)
Sent off: Krsticic 46 (S)