Marshall denied Shane Long a late equaliser to secure the three points.
"I didn't fear the worst because I knew my keeper would save it," said the Scot.
"Shane Long is someone who has scored regularly and he got hold of it well. But David Marshall has been immense for me, that was a top, top save.
"He was the best goalkeeper in the Championship last year and had certain challenges last season in terms of his ability getting back in the Scotland squad and being the number one goalkeeper in the Championship. Now we are seeing he is a proven Premier League goalkeeper.
"He has done a lot of work with our goalkeeping coach Jim Holman and we have a real belief in him and he brings a calmness to our back four which is noticed as well because the back four were tremendous again."