Heed inflicted Orient's ninth defeat of the season and they are now nine games without a win in the National League - watch match highlights here.
Burrow put Gateshead after ten minutes and then struck again in the 80th minute to all but wrap up the points and reward the loyal travelling fans.
"Firstly I'd like to thank the fans for coming out it's a long way for a Tuesday night and they were in great numbers," said the goalscorer.
"They've come in good numbers to be fair to them and that result was for them, I think we played well in patches and to get an early goal settled the nerves.
"They put a lot of pressure on us second half and as a team, the defence stood strong and we bagged that second goal it was effectively game over.
"The gaffer has a different style of training and a different way of playing so it's taken some time to adapt but hopefully we can kick on.
"It was good for me on a personal note to get a brace, there's been a few games where I've scored one but hopefully I can keep it up."