Warriors had been aiming to maintain the momentum they had gained after last week's impressive win over Leinster, yet they put in a very flat performance, managing to muster a sole Duncan Weir try, along with kicks from Weir and replacement fly-half Scott Wight, who missed a gilt-edged chance late on to steal the win.
It was the hosts who were first to get off the mark, a flowing move creating sufficient space for Weir to squeeze over in the corner for a self-converted score.
Treviso fly-half Kristopher Burton soon had his side on the scoreboard, however, atoning for an early penalty miss with a successful attempt on 20 minutes.
Glasgow's frequent indiscipline at the breakdown was proving to be costly, and their cause was not aided when, midway through the half, they were reduced to 14 men, hooker Pat MacArthur ordered to the sin-bin for excessive use of the boot at a ruck.
From the resulting penalty, Burton reduced the Warriors' lead to a single point with an accurate penalty effort.
Despite arguably having less of the play, it was the Italians who went into the break with the scoreboard in their favour, a further Burton penalty on the stroke of half-time handing them the advantage.
If the first half had been a drab affair, the second period was increasingly stodgy, the pernickety approach of referee Alan Falzone preventing the game from developing any flow or rhythm and restricting scoring opportunities.
Weir and Burton traded penalties to ensure the Italians maintained their two-point advantage heading into the final quarter, despite having played a period with reduced numbers, with captain Antonio Pavanello serving time in the bin for repeated offences at the breakdown.
The home side did have the chance to regain the lead after a period of sustained pressure, but Weir skewed his penalty attempt horribly wide.
With the Warriors firmly in the ascendancy it was only a matter of time until they had their noses in front once again, and a calmly struck penalty from replacement Wight secured the hosts a slender advantage heading into the final throes.
Yet that advantage was short-lived, the boot of Burton once again proving to be accurate as he coolly slotted a drop goal.
Tensions ran high in the closing stages as Glasgow became increasingly riled by a number of decisions handed down by Falzone, and their state of mind was not helped when Wight's drop goal attempt flew wide of the mark.
And it was the former Melrose man who had the last opportunity to snatch the win for his side, but from only 15 metres out his effort on goal sailed wide of the left-hand upright.
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