The Swans are a point clear of arch-rivals Cardiff in third and two ahead of Forest in fourth, although they do have a game in hand over both Welsh clubs.
Nestor and Zimonjic, who saved one match point to defeat arch rivals Bob Bryan and Mike Bryan in Saturday's semi-finals, were pushed all the way in the opening set before easing through to triumph in this end-of-season tournament for the second time in three years.
Joe Kinnear, confirmed as Newcastle manager until the end of the season 24 hours before kick-off, will be happy with a point that takes them out of the bottom three of the Premier League as arch-rivals Sunderland fall into the drop zone.