First-half tries from Phil Burleigh, Damien Hoyland and Sam Beard had given the visitors an 18-point lead, but scores from Andrea Pratichetti and Duncan Naude either side of half-time brought Treviso back into the contest.
Man of the Match Jayden Hayward was reliable with the boot, kicking his fourth successful penalty to level the game on 56 minutes.
But after Tonks' winning kick eight minutes from time, Solomons was delighted with his side's resolve in the blistering heat and after a tricky coach journey almost made them late for the game.
"We started hitting the fatigue at the end of the first half and we also picked up a yellow card. That impacted into the second half and further on," he told the Herald Scotland.
"The tough trip played a big role, it was just one of these things that happened. But the guts the guys showed to win the game was incredible, absolutely incredible.
"The courage to hang on through scrums on our line, to scrum with seven forwards and still win a penalty to kick it out, win a line-out and end the game - that's huge.
"It is a massive win for us. We need a break, this is the right time."
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