Kuchar and Harrington both carded four-under-par 68s to join MJ Daffue and Roberto Diaz at the top of the leaderboard when play was halted at The Oaks course in San Antonio.
Kuchar, who is chasing his first PGA Tour win since 2019, relished the challenge of the demanding Oaks layout.
"It's a tough golf course but I do like it," Kuchar said. "If you start playing some indifferent golf, this course can really jump up and bite you. I was lucky to get away with a couple of loose ones today."
Thursday's first round had got off to a chaotic start with play delayed by more than three hours early on due to thick fog.
Around half of the field were yet to finish their first rounds when play was suspended for the day in gloomy conditions.
Justin Lower was at five-under through nine holes when players were brought back in.
South Africa's Daffue meanwhile forced his way into a share of the clubhouse lead with a brilliant eagle three on the par-five 18th.
Daffue reached the green in two and then calmly rolled in a 14-foot putt for an eagle and a share of the lead.
"It was a good day," Daffue said. "I didn't necessarily have all my good ball-striking beginning of the round, and obviously with the rain and everything it was kind of tough.
"I've been in positions like this and just told myself like keep grinding."
Diaz meanwhile also joined the leaders after picking up a shot on the 18th, the Mexican journeyman sinking a 14-foot birdie putt on the last.
England's Matt Wallace was among a group of five players who are a shot off the clubhouse lead on three under.
