A knee injury had meant Hazard was doubtful for the contest at Solna's Friends Arena, creating concern for Belgium supporters with their FIFA World Cup opener versus Algeria just over two weeks away.
But the Chelsea winger put those worries aside, his 79th-minute strike adding to Romelu Lukaku's effort as Marc Wilmots' claimed a solid victory.
The head coach would also have taken great heart from Lukaku's goal, as he found the net with a stunning controlled finish from range to follow up a hat-trick against Luxembourg earlier this week.
Yet Belgium responded well and, suddenly attacking with purpose, came agonisingly close to breaking the deadlock when Kevin De Bruyne's precise curler rattled the woodwork.
It was all one-way traffic thereafter, with Kompany narrowly volleying over after meeting Dries Mertens' corner.
It was only thanks to a superb stop from the goalkeeper that Sweden did not find themselves 2-0 down, Isaksson getting down low to keep out Daniel Van Buyten's point-blank header from Mertens' deep cross.
Unwilling to give up, Erik Hamren's side saw off the danger before showing some attacking intent of their own.
Indeed, Thibaut Courtois' goal was under siege for long periods towards the end, Jimmy Durmaz hitting the woodwork with a vicious strike.
