Söderling, seeded fourth, advanced in front of a full house at the Kungliga Hallen arena with a 7-5, 6-3 defeat of German Benjamin Becker. After a combative opening set, the Swede rolled in the second to go through.
Björkman, 36, is preparing to retire this year and likely played his last singles match when he lost in the first round to Juan Monaco.
But his doubles is set to continue through the Madrid and Paris Masters event and hopefully the season-ending Masters Cup in Shanghai with partner Kevin Ullyett.
The Swede, with a 698-302 record, stands fifth on the all-time list for most doubles matches played, with retired Czech Cyril Suk heading the table on 1,147.
Two-time champion Thomas Johansson became a Swedish victim, falling to Spaniard Albert Montanes 6-3, 4-6, 6-3. Oscar Hernandez upset Argentine sixth seed Jose Acasuso 2-6, 6-3, 6-4 in the second round.
Third seed Jarkko Nieminen began his ninth straight appearance as he battled into the second round over young Brazilian Tomaz Bellucci 6-7 (5/7), 6-3, 7-5.
The flying Finn ranked 33rd in the world has twice gone to the Swedish final at a tournament the man from across the Baltic considers his home event.
But the 27-year-old is keen finally to snaffle the title after flirting with the trophy in 2001 and 2006 when he lost to Sjeng Schalken and James Blake respectively.
Nieminen fired 11 aces to the 10 of the 80th-ranked Bellucci in the two-hour, 20-minute struggle which put the third seed into a contest against the winner from Frenchman Arnaud Clement and Swedish qualifier Björn Rehnquist.
Nieminen said he got perhaps more than he bargained for against Bellucci, who now stands 4-15 this season.
“It was very tough, I didn’t believe he could serve so well,” said the Finn. “I was too passive in the beginning but I managed to get more aggressive in the second set.
“I just kept thinking positive and fought to the end.” Nieminen improved to 12-8 in Stockholm, where he frequently trains. The Finn is hoping to start improving a dismal record in finals (1-7 record) as he plays in familiar surroundings.
Swiss veteran George Bastl, also emerging from the qualifying ranks, won his first match since mid-July as he outlasted Dane Frederik Nielsen 7-6 (8/6), 3-6, 7-6 (7/4).
Bastl, whose claim to tennis fame came as the man who ended the career of Pete Sampras at Wimbledon (2002 second round) has suffered five straight ATP-level defeats since his first-round win in Los Angeles.
French 2001 Australian Open finalist Arnaud Clement defeated qualifier Björn Rehnquist 6-2, 6-1 while German Rainer Schüttler earned the first of the quarter-final spots 7-6 (8/6), 6-3 over Nicolas Lapentti of Ecuador.
Top seed David Nalbandian, playing after the withdrawal of Roger Federer, had the day off before tackling home hero Joachim Johansson in the second round.
The Swede, 26, reversed his 2007 retirement a year after quitting the game with a shoulder injury, making a winning return on Tuesday over Nicolas Mahut.