Connor cut it to 2-1 on a wrist shot off the rush from the right circle at 3:48 of the second period.
Anaheim killed four straight penalties before getting its first power play. Henrique deflected in a shot from Cam Fowler with five seconds left on the penalty for a 3-1 lead at 13:20.
Rakell, playing his 500th NHL game, scored a power-play goal off a deflection to make it 4-1 at 6:20 of the third period.
The Ducks were last in the NHL in power-play efficiency last season at 8.9 percent, the lowest since it became an official NHL statistic in 1977-78.
"We get a couple goals on the power play that we're not used to," Eakins said. "That pumps us along. The kid gets his first goal, which is awesome, 'Gibby' has an unbelievable night. There's a lot of great, feel-good things, and the guys are obviously fired up."
Winnipeg forward Cole Perfetti, the No. 10 pick in the 2020 NHL Draft, had one hit playing 9:49 in his NHL debut.
"It's a little different than how you dream about it as a kid," Perfetti said. "You dream about scoring your first goal and winning, but at the end of the day you're playing in the NHL. It's something I've worked hard for my entire life."
NOTES: Forward Mark Scheifele, who led the Jets with 63 points (21 goals, 42 assists) in 56 games last season, served the final game of a four-game suspension for charging Montreal Canadiens forward Jake Evans in Game 1 of the Stanley Cup Second Round on June 2. ... Defenseman Nate Schmidt had three shots and was plus-1 playing 23:59 in his Jets debut after being acquired in a trade with the Vancouver Canucks on July 27. … Forward Evgeny Svechnikov made his Jets debut after signing a one-year, two-way contract on Wednesday. He had one shot in 6:43 of ice time. ... McTavish is the youngest forward and second-youngest player in Ducks history to appear in a game. Defenseman Oleg Tverdovsky was 18 years, 248 days on Jan. 21, 1995 against the original Winnipeg Jets. … Ducks forward Benoit-Olivier Groulx made his NHL debut. The second-round pick (No. 54) in the 2018 NHL Draft had two shots and two hits in 14:30. ... Henrique's goal was his 400th NHL point. He has 199 goals and 201 assists in 711 games in 12 seasons with the Ducks and New Jersey Devils. … Isac Lundestrom and Jakob Silfverberg each had two assists for Anaheim.