Nov. 3, 2021, 3:18 a.m. ETNov. 3, 2021, 3:18 a.m. ETGlenn Youngkin after defeating Terry McAuliffe in Virginia on Tuesday.Melissa Lyttle for The New York TimesGlenn Youngkin, a Republican business executive, marched to victory in Tuesday’s election, delivering his party the governorship of Virginia and highlighting a strong night for Republicans less than a year after voters pushed them fully out of power in the nation’s capital.The outcome in Virginia, combined with an unexpectedly close contest in New Jersey, where the governor’s race remained too close to call, delivered a jolt of encouragement for Republicans and a stark warning sign for the Democrats less than 10 months into President Biden’s term.Mr. Biden’s approval rating has sagged to new lows as Democrats on Capitol Hill have struggled to coalesce behind his legislative agenda. The latest election results suggested an ominous erosion of the support in the suburbs that had put the party in power.Here are five takeaways from Tuesday’s contests and what the results could mean for 2022, when control of the House, Senate and 36 governorships will be on the ballot:Youngkin’s success across the state offers a G.O.P. pathway.Republicans suffered repeated down-ballot losses in the past four years, as the party grappled with how to motivate a base deeply yoked to Donald J. Trump without alienating the suburban voters who came to reject the former president’s divisive style of politics.Enter Glenn Youngkin and his fleece vest.Mr. Youngkin pulled off something of a surprise and rare feat: He drove up the Republican margins in white and rural parts of the state further than Mr. Trump had, cutting into the edge of the Democratic nominee, former Gov. Terry McAuliffe, in suburban areas. He even flipped some key counties entirely.Mr. Youngkin won in Chesterfield County, outside of Richmond, and Stafford County, an exurb of Washington, D.C., both places that Mr. Biden carried in 2020.And in conservative southwestern Virginia, Mr. Youngkin was topping 80 percent in heavily white and rural counties — up substantially from the Republican showing in the last governor’s race.