The 12th seed, who captured the Australian Open title in 2002, will now face either America’s Andy Roddick or Sebastien Grosjean for a place in the final, just two years after it seemed his career was finished.
The 30-year-old missed the entire 2003 campaign following knee surgery but recovered well to clinch his eighth career title in Stockholm at the end of last year.
He made the semi-finals at Queen’s Club before a groin injury forced him to retire from his second round match at Nottingham.
But he showed no ill-effects of his various problems on Wednesday as he followed in the footsteps of compatriot, and former double Wimbledon champion, Stefan Edberg who was the last Swede to make the last four in 1993.
“It feels unreal to be in the last four but I’m very happy with the way I played today,” said Johansson.
“It’s a lot of fun to be in the semi-finals but I am a long way away from Stefan Edberg. He played serve-and-volley, I’m more like Mats Wilander in that I stay on the baseline all the time.
“But I guess that’s an indication of how slow the courts are.”
Johansson broke in the third game of the first set to lead 2-1 before Nalbandian, the 2002 runner-up, levelled in the eighth game.
The Swede built up four set points in the tiebreaker and grabbed the opener after 73 minutes of vicious baseline hitting when the big Argentinian smashed a forehand wide.
He then edged ahead 2-0 in the second set and was soon 5-2 in front thanks to a confident love service game and then clinched the set 6-2 after Nalbandian’s service game once again fell apart.
The Argentinian had come back from two sets down to beat Britain’s Andrew Murray in the third round on Saturday and he briefly showed some fight by breaking the Swede in the first game of the third set.
However, the 23-year-old South American was unable to take advantage by allowing Johansson to break straight back at 1-1.
The Swede served a love-game to go 2-1 and then recovered from 0-40 down to break a dispirited and misfiring Nalbandian to edge 3-1 in front.
Johansson then secured his place in the last four on his first match point when his opponent netted a simple drive after 2hr 17min on court.