Yasin Ayari set the tone after just seven minutes, pouncing on a loose ball after Viktor Gyokeres had forced a save from the Tunisian goalkeeper. Alexander Isak doubled the lead in the 30th minute with a composed solo finish.
Tunisia responded just before the break when Omar Rekik headed in to make it 2-1, briefly threatening a route back into the contest. Any hopes of a comeback were extinguished early in the second half.
Gyokeres restored the two-goal cushion in the 59th minute, turning home after Isak had set him up. Substitute Mattias Svanberg then made an instant impact, scoring within seconds of coming on to make it 4-1, a goal that survived a lengthy VAR review for offside.
Ayari completed the rout with the final kick of the match, driving home from distance for his second of the night. He chose not to celebrate either of his goals, a gesture rooted in his family connection to Tunisia through his father.
Speaking to ITV after the final whistle, Sweden head coach Graham Potter could barely contain his satisfaction with the performance.
"Fantastic. Great goals, five goals, solid and we could have scored more. It was brilliant, full credit to the players. They were fantastic."
Potter, who took charge of the Swedish national team last October after a difficult qualifying campaign that required a play-off route to reach the tournament, addressed Tunisia's goal and how his side responded.
"It came from not that much really. It can happen in football. The boys remained calm and maintained a goal threat which was important for us."
He struck a note of caution despite the scoreline, mindful of the tougher tests still to come in a group that includes the Netherlands and Japan, who played out a dramatic 2-2 draw earlier in the day.
"There is room to improve. We will enjoy tonight, recover and get ready again."
For Tunisia, the result represents a damaging start to a campaign built on a reputation for defensive solidity through qualifying. Conceding five goals in an opening match leaves little margin for error against opponents who will have taken note of the gaps exposed in Monterrey.
Sweden's victory pushes them two points clear of both the Netherlands and Japan at the top of Group F, and offers genuine encouragement for a squad that arrived in North America with modest expectations after a turbulent route to qualification. Potter's side now have breathing room heading into their next assignment, but the manager's measured tone after such a dominant win suggests he is already focused on what comes next.