Sidwell scored the opening goal and despite the Magpies equalising through a fantastic strike from Hatem Ben Arfa, Hugo Rodallega headed in a winner on 63 minutes.
Fulham remain in 13th place in the Premier League table but they have now pulled away from Newcastle and are seven points above third-from-bottom Sunderland.
"It was massive. In the table before the game there was a bit of a gap between us and the teams above so it was important for us to get the three points and keep in touch," Sidwell told Sky Sports.
"We came out of the traps first half and got the goal. The second half they really pushed us and got the equaliser but Hugo popped up with a header and we hung in there."
Sidwell's goal took a deflection on its way in but the former Chelsea player insisted he will battle to have it recorded as his own.
"It was definitely going on target so if they don't give it to me, I am after that dubious goals panel," he added.