Chris Wagner and Ryan Kesler also scored for Anaheim, which has earned points in 13 consecutive games since March 10 (10-0-3).
With the best record in the West already sewed up, the Central Division champion Blackhawks rested captain Jonathan Toews, forwards Marian Hossa and Artem Anisimov and defensemen Duncan Keith, Brent Seabrook and Niklas Hjalmarsson.
Corey Crawford stopped 22 shots in Chicago’s third straight loss.
Gibson made several outstanding stops in his first back-to-back starts since mid-February, appearing to be fully recovered from his nagging injuries. The shutout was his sixth of the season.
The Ducks played without injured defensemen Cam Fowler and Hampus Lindholm. Fowler will miss at least the start of the playoffs after an unpenalized knee-on-knee hit from Calgary captain Mark Giordano on Tuesday, while Lindholm could return this weekend from an unspecified upper-body injury.
Anaheim played with one eye on the scoreboard in San Jose, where the Sharks and Edmonton Oilers jockeyed for second place in the Pacific.
Only the Oilers have a mathematical shot at catching the Ducks. Anaheim’s victory clinched a top-two finish and home ice in at least the first round.
Perry put the Ducks ahead in the first period by converting Rakell’s pass into a power-play goal, his eighth score in 15 games after a painfully slow start to his season.
Perry also drew the Blackhawks’ ire when he slashed Ryan Hartman after the whistle late in the first period. Perry got a minor penalty on the play.
Wagner scored his sixth goal of the season late in the second period on a remarkable pass from Ondrej Kase.
Kesler scored his 22nd goal after a no-look, behind-the-net pass from Andrew Cogliano early in the third.
Ducks forward Nick Ritchie got a match penalty moments later for his one-punch knockdown of Michal Roszival, who had just cross-checked Perry behind the Chicago net.
Rakell added the 33rd goal of his breakout season in the final minutes, making a backward tip of Ryan Getzlaf’s shot.
Defenseman Jaycob Megna made his NHL debut for the Ducks. The Chicago-area product has scored 44 points and leads the AHL with a plus-55 rating this season for the Ducks’ top affiliate in San Diego.
NOTES: The Canucks were the last NHL team to win five consecutive division titles, dominating the Northwest Division from 2009-13 before NHL realignment put Vancouver in the Pacific. Detroit won eight straight Central Division titles from 2001-09, sandwiched around the 2004-05 lockout. … Megna, the younger brother of Vancouver forward Jayson Megna, was a seventh-round pick in 2012. He is the 12th defenseman to play for Anaheim this season. … Chicago and Anaheim are the only teams to top 100 points in each of the past four seasons.
Blackhawks: At Kings on Saturday.
Ducks: Host Kings on Sunday.
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