Townsend has come under fire after a poor start to the tournament for Scotland, who lost their opening two games against Ireland and England without scoring a try.
Captain Stuart Hogg ended that drought to put Scotland ahead at the Stadio Olimpico on Saturday, and Chris Harris' second-half effort made it a 10-point gap that proved well beyond the hosts, who conceded a third try to Adam Hastings in the last minute.
The score was Scotland's largest win in Rome but there was still plenty unconvincing about their performance and Townsend will still have plenty of work to do to win over the doubters, while Italy appear destined for another wooden spoon.
— Scottish Rugby (@Scotlandteam) February 22, 2020
Scotland spent much of the opening exchanges on the backfoot after Hastings missed what looked a simple early penalty as Italy made the majority of the early running.
For all their energy, Italy lacked composure with ball in hand and were punished for failing to capitalise on their early pressure in spectacular fashion by Hogg.
Hogg picked the ball up in his own half and weaved his way past Jake Polledri and Jayden Hayward before surging down the right to dive over in the corner.
Ali Price saw a try chalked off for a forward pass in the build-up before Tommaso Allan struck the post from the tee for the hosts.
Harris crashed over from close range to double Scotland's advantage six minutes into the second half, but Hastings again failed to add the extras.
Marco Riccioni was taken off on a cart in a blow to an Italy side that continued to spurn attacking openings and when Federico Zani was sent to the sin bin for a dangerous tackle their hopes were effectively ended.
Hastings then scooted down the blind side to add last-minute gloss to the scoreline, with Italy nilled for the second time in three matches.
Hogg leads by example
Scotland were second best in the opening 20 minutes, but skipper Hogg lifted their spirits and turned the tide with a fine individual effort that marked a moment of quality in a game otherwise short on it.
Italy lack killer instinct
Italy crafted a plethora of promising openings with a series of line breaks, but their inability to finish those attacks off was the decisive factor in a tight affair.
Photo Getty Images Caption: Stuart Hogg scores for Scotland