Van Hollen, a two-term state senator from Montgomery County, won a close contest in the 8th Congressional District, though Shriver raised twice as much money - a whopping $2.5 million.
In other U.S. House races, Baltimore County Executive C.A. Dutch Ruppersberger held off a spirited, deep-pocketed challenger in the 2nd District Democratic primary and will face former Rep. Helen Delich Bentley in the November election.
It was a night in which all of the state's U.S. House incumbents prevailed, including six-term Rep. Wayne T. Gilchrest, who was tested by a conservative opponent.
Gilchrest defeated Dave Fischer 3 to 2 in the 1st District, which includes all nine Eastern Shore counties and parts of three other counties.
It was well after midnight when Van Hollen, 43, thanked his supporters at a Chevy Chase victory party for their "spirit and commitment." He said he had received a "very, very gracious" phone call from Shriver conceding defeat.
"Take a day off, but then we really have serious work to do," Van Hollen, who will face Republican Rep. Constance A. Morella, told supporters. The crowd members stamped their feet and chanted "Chris, Chris, Chris."
Shriver is the nephew of President John F. Kennedy - and a member of a family that rarely loses elections.
Before conceding, Shriver addressed a crowd of supporters before midnight, telling them he was "cautiously optimistic." The crowd included his uncle, Sen. Edward M. Kennedy, and his sister, TV newswoman Maria Shriver.
Despite wide name recognition, Ruppersberger didn't enjoy a comfortable win - he had 50 percent of the vote to businessman Oz Bengur's 36 percent. Three other Democrats ran in the primary, but none garnered significant support.
Ruppersberger set his sights on Congress a year ago as his hopes for a gubernatorial bid dimmed. He made it known last fall that he would run for a seat if Gov. Parris N. Glendening would use redistricting to draw a new district favorable to Democrats. He did.
Bentley overcame token Republican opposition yesterday.
No U.S. House incumbents were knocked off in Maryland in the 2000 election, and none besides Gilchrest was seriously challenged last night. This year, there is an open seat - in the 2nd District - vacated by Republican Robert L. Ehrlich Jr., who is running for governor.
Democrats say they believe that seat, along with one held by Morella in the 8th District, gives the party opportunities to gain ground on the Republicans in the fall election. Currently, Democrats and Republicans split the eight congressional seats in Maryland.
In Gilchrest's district, Fisher, 32, who pumped more than $300,000 of his own money into his campaign, forced the veteran and self-described moderate into a lively primary.
The race drew national attention, including a flurry of television and radio ads for Fischer produced by the Washington-based Club for Growth, a conservative, anti-tax group that has drawn fire for helping to challenge an incumbent.
Television spots have been running on Salisbury and Baltimore stations in recent weeks with the tag line, "Gilchrest, shockingly liberal."
Gilchrest portrayed himself as a "real Republican."
"I think this election shows that it's very difficult to fool people," Gilchrest said after he won. "We've learned a lot from this race, and we'll be better for it. In this kind of primary, we thought 60 percent would be good, and we've done that."
Fischer spokesman David Talley said the challenger would not comment until all votes were counted.
Outspent by Fischer and the Club for Growth, which raised more than $100,000, Gilchrest, 56, leaned heavily on support from party regulars and endorsements from President Bush and gubernatorial candidate Ehrlich.
Gilchrest, who since 1993 has refused to accept donations from outside his district, was backed by moderate legislators from the Republican Main Street Partnership.
The coalition raised more than $100,000 in defense of "one of our own," backing Gilchrest with an independent advertising blitz that the Fischer campaign says amounted to a violation of Gilchrest's self-imposed ban on outside contributions.
The Shriver-Van Hollen race became one of the state's most closely watched.
With more than $6.5 million raised among the three Democrats and Morella, the race is the most expensive of the nation's 435 House districts, according to the Center for Responsive Politics, a watchdog group. Much of the Democrats' money went to television advertising in the Washington market, where it cost candidates about $400,000 to compete in the final week.
It was a relatively polite race until the last week, when Shriver, a state delegate, released a TV spot accusing Van Hollen of misrepresenting Shriver's state legislative record in voter mailings.
A third candidate, Ira Shapiro, a former Clinton administration trade representative, sought to take advantage of the scrap, running a TV ad depicting two young boys - meant to represent his main rivals - flailing away at each other with boxing gloves.
According to a recent Sun poll, Shriver's most effective argument was that he had the best chance of the three to unseat Morella, an eight-term incumbent who had her toughest re-election fight two years ago. The man she beat in 2000, Terry Lierman, recorded a telephone message for Shriver in this election, saying he was the party's best hope against the popular Republican, whose campaign signs read simply, "Connie."
But Van Hollen seemed to gain momentum at the end of the race, picking up endorsements from the Washington Post and The Sun. His campaign handed out thousands of copies of the endorsements at Metro stops and spread the word with about 45,000 phone calls to likely Democratic voters in the district in Montgomery and Prince George's counties.
Sun staff writers Andrew A. Green, Chris Guy and Sarah Koenig and special correspondents Ayesha Ahmad and Catherine Matacic contributed to this article.