The study for BBC Scotland found that 72% of those questioned think it has done well and just 15% think it has handled the situation badly, while 12% say it has done neither well or badly and the remainder do not know.
A similar Ipsos Mori poll conducted in May found that 78% of respondents said the Scottish Government was doing well and 11% badly.
Meanwhile, only a quarter (25%) of the 1,037 Scottish adults questioned said they think the UK Government has handled the pandemic well, while more than half (55%) think it has done badly, the November poll found.
Only 19% of those questioned said Prime Minister Boris Johnson has handled the crisis well, while 62% said he has handled it badly.
However, almost three-quarters (74%) of respondents believe First Minister Nicola Sturgeon has handled the pandemic well, while only 13% say she has done so badly.
This compares with a similar poll in May where 82% felt she was dealing with it well and just 8% felt she was handling the situation badly.
The research also found that 64% of people who voted No in the 2014 independence referendum believe the Scottish Government has handled the pandemic well, while more than two thirds (65%) say the same of Nicola Sturgeon.
In this group less than a third (31%) believe the UK Government has addressed the pandemic well, while just more than a quarter (26%) say the same of Boris Johnson.
The Ipsos Mori poll was conducted by telephone between November 10 and 15.
The survey also asked people what they think about the coronavirus restrictions, with six in 10 (62%) saying they think the restrictions where they live have until now been “about right”.
Almost two in 10 (19%) think they are “too strict” while 17% think they are not strict enough.
However, almost half (49%) said they believe the Scottish Government was “too late” to tighten the coronavirus restrictions.
Just over four in 10 (42%) said they think the timing was about right, while 5% said that it was too early.