The Warriors trailed for much of the opening half until efforts by Liam Marshall and Bevan French, who also had a hand in two second-half tries, before the interval handed the 2025 grand final runners-up a slender advantage at the break.
Eckersley's 43rd-minute try cemented Wigan's grip on proceedings before he added another and Jake Wardle made the points safe when he crossed 13 minutes from time. Castleford rallied late on, but they had too much to do.
After a weekend of surprise results, with champions Hull KR defeated, Wigan looked set to suffer the same fate when Liam Hood opened the scoring after 10 minutes.
It stayed 6-0 until the 34th minute when Marshall grabbed the first of five tries for the Warriors before French finished off a slick move to ensure the visitors were 10-6 up at halftime.
Matt Peet's men were in the ascendancy and Eckersley opened his account three minutes into the second half before he virtually wrapped up the points with a second score after 62 minutes.
It was followed by a try for Wardle, but the Tigers finished strongly after Wigan's Adam Keighran was sent to the sin bin, with Mikaele Ravalawa and George Lawler able to add consolation efforts in the final 11 minutes.
"For large parts defensively I thought we were very good against a team who certainly asked questions," Wigan chief Peet told the official club website.
"I liked our last plays and at times when we got going with the ball we were decent. We will get better."
Tigers boss Ryan Carr told BBC Radio Leeds: "If we ... didn't make the game of footy so hard on ourselves the scoreline would have been much closer coming into the last 20.
"They've (Wigan) been together a long time, they're well drilled and they know what they're doing.
"We knew we were in for a fight, but we were definitely up for it. We just didn't manage the game well at certain times."
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