Kewell took over after Australian compatriot Kevin Muscat resigned at the end of the 2023 season, and goals from Elber and Kota Watanabe on Wednesday gave him the perfect start as Marinos enjoyed a two-goal cushion inside the opening 24 minutes of the first leg encounter at Thammasat Stadium.
But Nitipong Selanon pulled one back 10 minutes from the interval and Eid equalised two minutes into stoppage time as he powered a header home.
It was a frustrating finale for Kewell, who has taken the reins after a spell as Ange Postecoglou's assistant when the Spurs manager was still at Celtic.
Elber scuffed the ball over the line in the 18th minute to put the Japanese side ahead after Nam Tae-hee's cross and Watanabe doubled the lead six minutes later when Anderson Lopes deflected Ren Kato's cross into the midfielder's path.
With 10 minutes left in the half, Nitipong halved the deficit when he evaded two challenges to slip the ball between the legs of Marinos goalkeeper William Popp.
Substitute Ryo Miyaichi missed a late chance to make the result safe for Marinos and Eid punished the J.League side when he met Nitipong's cross from the right with a decisive finish.
Marinos' Ken Matsubara was sent off for a two-footed lunge on Vander Luis with seconds remaining and the teams will meet in the return leg in Yokohama next Wednesday.
Elsewhere, Jeonbuk Hyundai gained the upper hand in their all-South Korean battle with Pohang Steelers at Jeonju World Cup Stadium as goals from Hernandes and Ahn Hyeon-beom earned Dan Petrescu's team a 2-0 first leg advantage.
Hernandes gave the twice champions the lead in the 17th minute when he smashed his close-range shot in off the underside of the crossbar after Hong Jeong-ho had earlier thumped the woodwork with an effort from distance.
Pohang threatened to come back into the game in the second half, with substitute Jorge Luiz causing problems for the home side.
But Ahn's diving header in the 64th minute means Jeonbuk will go into next Wednesday's second leg at Pohang Steel Yard with a two-goal advantage.
