Goodling appeared to be in trouble in the weeks leading up to Tuesday's primary, but he easily beat conservative lawyer Charles Gerow, getting 68 percent of the vote to Gerow's 32 percent.
Arkansas and Oregon also had primaries Tuesday.
In Oregon, disgraced former Republican Rep. Wes Cooley failed in his bid to reclaim the seat he abandoned two years ago after it was revealed he had lied about fighting in the Korean War. Cooley finished third in a four-way race.
The winner was Greg Walden, a broadcaster and former state legislator, who got 56 percent of the vote.
In Arkansas, state Sen. Fay Boozman got 78 percent of the vote to defeat former Little Rock Mayor Tom Prince for the GOP Senate nomination.
Boozman won't know his Democratic opponent until June 9, when the top two finishers in Tuesday's primary meet in a runoff.
Former Rep. Blanche Lincoln - who quit after two terms in 1996 after having twins - got 46 percent of the vote, falling short of the majority needed to avoid the runoff. She'll face Attorney General Winston Bryant, who got 27 percent in a four-way field. The seat is open because Democrat Dale Bumpers is retiring.
Computer trouble in suburban Philadelphia delayed final election results, but with 98 percent of precincts reporting, two-term Rep. Jon Fox - with 49 percent of the vote - appeared to have easily defeated three primary challengers.
If those numbers hold, Fox will again face Democrat Joseph Hoeffel, who lost to Fox by only 84 votes in 1996.
In a special election in Pennsylvania's 1st District, which includes part of Philadelphia, Bob Brady, the city's Democratic chairman, was elected to replace Democratic Rep. Tom Foglietta, who resigned to become U.S. ambassador to Italy.
Most of the high-profile incumbents in the three states had an easy time in their primaries:
In Oregon, Democratic Sen. Ron Wyden was nominated for a full term. The GOP nominee is state Sen. John Lim.
Democratic Gov. John Kitzhaber, seeking a second term, easily won the primary. The Republican nominee is tax watchdog Bill Sizemore, who overcame reports about his trail of debt.
In Pennsylvania, GOP Gov. Tom Ridge, seeking a second term, was unopposed. State House minority whip Ivan Itkin beat two rivals for the Democratic nomination.
Three-term Republican Sen. Arlen Specter and Democratic state Rep. Bill Lloyd each beat two rivals for the nomination.
In Arkansas, Gov. Mike Huckabee won the GOP nomination. He's running for governor for the first time after inheriting the office in July 1996 from Jim Guy Tucker, who was forced to resign after being convicted in the Whitewater scandal. Democrat Bill Bristow, the lawyer representing the state trooper in the Paula Jones case, waunopposed.
By Ned Kilkelly