Not that long ago, Alex Caicedo was stuck working a series of odd jobs and watching his 1984 Chevy Nova cough its last breaths. He could make $21 an hour at the Johnny Rockets food stand at FedEx Field when the Washington Redskins were playing, but the work was spotty.

Today, Mr. Caicedo is an assistant manager at a pizzeria in Gaithersburg, Md., with an annual salary of $40,000 and health benefits. And he is getting ready to move his wife and children out of his mother-in-law’s house and into their own place. Doubling up has been a lifesaver, Mr. Caicedo said, “but nobody just wants to move in with their in-laws.”

The Caicedos are among the 3.5 million Americans who were able to raise their chins above the poverty line last year, according to census data released this month. More than seven years after the recession ended, employers are finally being compelled to reach deeper into the pools of untapped labor, creating more jobs, especially among retailers, restaurants and hotels, and paying higher wages to attract workers and meet new minimum wage requirements.

“It all came together at the same time,” said Diane Swonk, an independent business economist in Chicago. “Lots of employment and wages gains, particularly in the lowest-paying end of the jobs spectrum, combined with minimum-wage increases that started to hit some very large population areas.”