WASHINGTON — Democrats enhanced their prospects for winning control of the House with Tuesday’s coast-to-coast primary results, skirting potential calamity in California and lining up likely gains in New Jersey and possible victories in Iowa and New Mexico.

The Democratic Party had feared disaster in California, where a quirky “jungle primary” gives the November ballot to the top two finishers, regardless of party. But Democratic contenders there leveraged financial and strategic help from the national party to weather the winnowing primary, and ensure that they will field candidates in multiple districts that they will most likely need if they are to win control in November.

“Even though Democrats had to spend a few million dollars, crisis averted,” said Nathan Gonzales, a veteran House race handicapper and the editor of the Inside Elections newsletter.

Republicans avoided their own worst-case scenario as well, securing a spot in the California governor’s race, which should help bring G.O.P. voters to the polls this fall to vote for their party’s House candidates. Republicans missed a slot on the ballot to challenge Senator Dianne Feinstein’s re-election bid, but a shutout in both California’s Senate race and its contest for governor could have severely depressed conservative turnout.