Mikael Lustig bundled in from a corner to double their lead, before substitute John Guidetti struck a late third.
Not even Bale's introduction could rouse Wales, who face Slovakia in their Euro 2016 opener on Saturday.
With Wales' first match at a major tournament for 58 years in mind, manager Chris Coleman could at least be consoled by the fact his players avoided serious injury in Stockholm.
But he may have been a little disappointed by a somewhat disjointed performance, which was perhaps to be expected with Wales having not played since a friendly defeat against Ukraine in March.
Relive Sweden v Wales
Zlatan v BaleThe fixture was billed as a battle between the two teams' stellar talents - Bale against Sweden's inspirational and outspoken captain Zlatan Ibrahimovic.
Bale had not featured for Wales since October and, having played 120 minutes of Real Madrid's Champions League final triumph the previous weekend, the 26-year-old was left on the bench.
Ibrahimovic, heavily linked with Manchester United after leaving Paris St-Germain, started the match and was predictably the orchestrator of every home attack.
His own efforts on goal were initially limited to a 25-yard shot which curled wide but, shortly before half-time, his elegant control and nonchalant pass teed up Forsberg to strike into the bottom corner.
Ibrahimovic had been substituted by the time Bale emerged, so their much-vaunted duel did not materialise.
Home and away fans alike were thrilled to see Bale and, although he showed flickers of his considerable threat, he could not revive Wales as Sweden eased to a comfortable victory, Coleman's side failing to muster a single shot on target.
Coleman's selection issuesWales already had fitness concerns about a handful of players ahead of this fixture, so Coleman was anxious not to add to his list of potential absentees.
Injured midfielders Joe Allen and Joe Ledley and striker Hal Robson-Kanu were rested with a view to them playing against Slovakia - remarkably in the case of Ledley, who broke his leg in May.
While Bale was on the bench, Jonny Williams impressed in the Real Madrid forward's usual roaming role in attack, with an inventive and energetic display.
There was also a first Wales appearance since October for Arsenal midfielder Aaron Ramsey, sporting a distinctive new blonde hairstyle and looking like one of his country's likeliest sources of a goal.
The match was a useful workout as Coleman ponders his team to face Slovakia, but the nature of the performance will have been less than encouraging as Wales embark on their historic campaign in France.
My Wales starting XI
Man of the match - Emil Forsberg
Manager reactionWales boss Chris Coleman: "We get a bit of success, a bit of expectation, sometimes a little bit of complacency and that can give you a little slap in the face.
"Maybe that's what's happened to us, certainly today. It doesn't mean we can't produce something special [at Euro 2016], because we're capable of it."
Read more from Coleman
AnalysisKevin Ratcliffe, former Wales and Everton captain on BBC Radio Wales
"The result won't bother Chris Coleman. It's all about the first game next week. That's what he's been building up to.
"He knows next week is a different kettle of fish. The last goal summed it up - Ashley Williams would have gone in harder if this was a competitive match. This was about getting the rustiness out, and I think they've achieved that."