WASHINGTON (AP) — The House voted Thursday to unlatch a gateway to citizenship for young Dreamers, migrant farm workers and immigrants who’ve fled war or natural disasters, giving Democrats wins in the year’s first votes on an issue that faces an uphill climb in the Senate.

On a near party-line 228-197 vote, lawmakers approved one bill offering legal status to around 2 million Dreamers, brought to the U.S. illegally as children, and hundreds of thousands of migrants admitted for humanitarian reasons from a dozen troubled countries.

They then voted 247-174 for a second measure creating similar...