Perron opened scoring just 1:12 in and Colaiacovo made it 2-0 five minutes later.
Berglund, who had 21 goals and 26 assists as a rookie last season, put the Blues ahead for good midway through the second session. Kariya scored within a span of 2:59 late in the period. Steen ended scoring late in the third.
"It was fun to be home and play, but I really expected Linkoping to play better and have a sellout crowd," Berglund said.
Berglund grew up on the larger European playing surfaces, but had some problems early on.
"It took some time to get adjusted, sometimes I had no idea where my teammates were," he laughed.
Berglund made a big adjustment last season, making the Blues' squad as a rookie after playing in "Allsvenskan", a second-tier minor league below the Swedish Elite League which is regarded as one of Europe's best.
Linkoping, a team which has been on ice since August, is eighth in the 12-team Swedish Elite League.