Four-term Senate veteran Howard W. Cannon (D-Nev.) led by 140 votes with 54 percent of the vote counted early today in a hard-fought primary challenge by a conservative Democratic "Boll Weevil" congressman who has supported most of President Reagan's economic measures.

Cannon led Rep. James D. Santini, who gave up the seat he has held as Nevada's only congressman for the last four terms to take on Cannon. The narrow vote see-sawed during the evening, with Santini narrowly leading much of the time.

The showdown was the most closely watched contest in the five western states holding primaries yesterday. They are Nevada, Colorado, Utah, Washington and Wyoming.

Cannon, 70, spent the campaign attacking Santini, 45, as a supporter of Reaganomics and pawn of the "big oil" interests that helped the challenger build a campaign war chest of $1.2 million, an unusually large sum for a primary in a state with such a small population.

Cannon also attacked the National Conservative Political Action Committee (NCPAC) for running ads against him that he said were filled with "lies and smears."

Santini depicted Cannon as a liberal out of step with the conservative instincts of most of the state's Democrats. He referred to the "integrity issue," a reminder that Cannon was investigated, though cleared, in 1980 of allegations that he had been bribed by a Teamsters union official.

He also criticized Cannon for never giving the voters a full disclosure of how he had become a millionaire while serving in the Senate. Age and seniority also were issues in the campaign.

On the Republican side, former state Sen. Chic Hecht won 38 percent of the vote to defeat developer Rick Fore.

In the gubernatorial primaries, GOP incumbent Robert List defeated two opponents, while on the Democratic side, Attorney General Richard H. Bryan took an early lead over Lt. Gov. Myron E. Leavitt and four others.

In a novelty race, former state senator Mary Gojack of Reno, a former blackjack dealer, won the Democratic nomination in the newly created 2nd Congressional District despite a bitter challenge from her former husband, John Gojack, who was trailing a large field. He named his dog as campaign manager, and denied that he was in the race as a spoiler. Colorado

Democratic Gov. Richard D. Lamm was unopposed for nomination to a third four-year term. His opponent in November will be Republican John Fuhr, a veterinarian and former state legislator who also had no primary opposition.

In the only contested race among six congressional primaries, former Apollo astronaut Jack Swigert handily defeated former combat pilot Norm Sothan for the Republican nomination to a new 6th District seat in the Denver suburbs. Swigert, who lost a bid for the GOP Senate nomination four years ago, now faces Aurora Democratic City Councilman Steve Hogan, who ran unopposed. Utah

Republican Sen. Orrin G. Hatch and Democratic Salt Lake City Mayor Ted Wilson were unopposed in party primaries yesterday, presaging one of the sharpest ideological clashes of the fall campaign.

Wilson, 42, will try to challenge as a middle-of-the-road Democrat who combines opposition to Reaganomics and advocacy of a nuclear freeze with opposition to gun control and abortion. He has been targeted for defeat by right-to-life groups.

Hatch, 47, is a fervent free-enterprise Republican who, as chairman of the Labor and Human Resources Committee, has pushed through bills calling for deep cuts in health, welfare, education and jobs programs.

In the state's newly created 3rd Congressional District, former state house speaker Howard Neilson defeated political newcomer Raymond Beckham, a communications professor, in the GOP primary. Neilsen will be the clear favorite in November over Democrat Henry Huish, a businessman who ran without opposition. Washington

Incumbent Democratic Sen. Henry M. Jackson, 70, easily defeated token opposition to his bid for nomination to a sixth term.

In the GOP Senate primary, Seattle City Attorney Doug Jewett, 35, won about 42 percent of the vote and defeated Seattle businessman Larry Penberthy.

In House races, the hottest primary was a four-way contest for the GOP nomination in the newly created 8th District, fashioned to elect a Republican. In early returns, state Rep. Rod Chandler led with 36 percent of the vote to 31 percent for state Rep. Bob Eberle. Incumbent Democrat Thomas S. Foley easily won the 5th District nomination. Wyoming

Democratic Gov. Ed Herschler easily won nomination to a third term over Pat McGuire, a rancher and political novice. In the GOP gubernatorial race, former state house speaker Warren Morton took a commanding early lead over over two opponents.

In the Republican Senate primary, incumbent Malcolm Wallop won renomination to a second term over rancher Richard Redland. He will face former state senator Rodger McDaniel, who ran unopposed in the Democratic primary.