HOUSTON — The Yankees were determined to sneak through this season with an economical rotation led by young ace Luis Severino and a cast of veterans and some key young arms to bridge the gap,

So confident were they in this plan that they gave Severino a four-year, $40 million extension in spring training.

All this may still work out, but things have changed.

The year came to a complete halt for Severino as the Yankees announced before Tuesday night’s house-of-horrors 6-3 loss to the Astros at Minute Maid Park that Severino is shut down for six weeks with what they say is a new injury, a Grade 2 lat strain.

Don’t forget Noah Syndergaard had a lat injury in 2017. He was injured April 30 and did not return until Sept. 23.

The Yankees don’t like to deviate from a plan, and that’s what it would take to sign frozen free agent Dallas Keuchel. Still, Keuchel is a proven winner and just threw 100 pitches in a simulated game.

They have CC Sabathia on tap, as well as Gio Gonzalez, who pitched six shutout innings Tuesday night at Triple-A Scranton/Wilkes-Barre.

Aaron Boone said with conviction after this ugly, ugly loss that his Yankees are close to getting it together.

“There’s no denying how important he is and how good of a pitcher he is,’’ Boone said of Severino, “but we’re also very close to making this thing run at a high level. There is no doubt in my mind and even in these two games some mistakes or plays that we didn’t make that we could have, swings the game.

“The bottom line is that we have gone up against two pitchers [Justin Verlander and Gerrit Cole] and have had leads late and just haven’t been able to hold them.’’

Signing Keuchel would be a bold move. The lefty is a proven winner and owns a 73-55 record in the AL with a 3.54 ERA.

Keuchel, 31, is battle-tested in October as well, with nine postseason starts and a 4-2 record with a 3.31 ERA.

He remains the free agent in limbo, represented by Scott Boras, and is becoming more popular by the day. The Dodgers lost starter Hyun-Jin Ryu to a left groin strain Monday.

“The Dodgers should be all over Keuchel,’’ a scout at the game told The Post on Tuesday night. That was about 90 minutes before the Yankees made the announcement that Severino will not touch a baseball for six weeks.

The Yankees should be all over Keuchel. They checked on him early in the free-agent period, but that was about it. They should take another look.

Adding Keuchel would be a bonus because the former Astro knows this Houston team’s makeup, and you just know if the Yankees can somehow salvage their starting pitching, they will meet the Astros in October again deep in the heart of Texas.

The 5-6 Yankees are fortunate the Red Sox (3-9) are in a post-World Series funk and their ace, lefty Chris Sale, is struggling (9.00 ERA), getting through only four innings in a 7-5 loss to the lowly Blue Jays on Tuesday in Boston’s home opener.

Houston had a much different starting pitching plan than the Yankees, and it helped win the World Series in 2017, beating the Yankees along the way in the ALCS when the series switched back here for the last two games, both won by the Astros.

They went out and landed Verlander when they already had Keuchel. This spring, they gave Verlander a two-year, $66 million extension.

They also beat the Yankees out in a trade with the Pirates for Cole in January 2018. Big arms stabilize a rotation.

As it stands now, this Yankees rotation does not scare anyone, and there will be many more nights like Tuesday when it will take at least six pitchers to get through a game.

Sure, you can build a bullpen and hope you have accumulated enough starting pitching depth, but the top two or three starters have to be your strength.

Keuchel may not fit into the Yankees’ plans right now, but he should.