For his first goal, Lukaku nodded in a sensational pass by Kevin De Bruyne.
Sweden is back at the World Cup for the first time since 2006, and its most famous player, Zlatan Ibrahimovic, retired from global competition after the European Championship.
A superb Dries Mertens strike just after the break and a Romelu Lukaku brace sealed an ultimately comfortable win for the Belgians in the Group G encounter in Sochi, as the Central Americans succumbed to a defeat in their first-ever match at the finals. Did those results influence the performance of the Red Devils?More news: Sri Lanka deny ball-tampering accusations, continue to play Test ‘under protest’
"It was tough. A long run-up to the World Cup and finally you have the first match and everybody expects so much", Martinez said. "I feel very confident".
The long odds have not tempered the excitement surrounding Panama's journey to Russian Federation, and the nation has proudly supported the team's achievement in simply qualifying for the World Cup.
Strength: Managerial experience. Boss Hernan Gomez is leading a third different team at a third different World Cup.
In other words, there is a lot stacked against Panama, which looked lackluster in its two pre-tournament friendlies, playing to a scoreless draw with Northern Ireland and losing 1-0 to Norway. "Panama played with dignity".More news: PM Modi salutes indomitable spirit of Afghanistan on Test debut
If Hazard, De Bruyne and Lukaku are allowed space and time to create, it could get ugly quickly for Panama. England's players will need no introduction to the majority of this Belgium squad and will be well aware of what Chelsea ace Hazard can do one his day.
Vermaelen, also 32, has been out since the middle of last month after suffering a hamstring tear in action for his club Barcelona.
Belgium start their World Cup campaign on more familiar ground: a squad stuffed with stars but with questions over their manager.
Martinez on Sunday said Hazard was ready to light up a tournament in the same way as Portugal's Cristiano Ronaldo did with his stunning hat-trick against Spain.More news: Second Sheriff’s Deputy Dies Following Shooting In Kansas
Belgium announced defender Laurent Ciman - who had travelled with his compatriots to Russian Federation as cover for the injured Kompany - left the squad on Saturday. Jaime Penedo in goal is 36, while Blas Perez up front is 37. Youth and speed may cause Panama problems.