Gov. Ella Grasso (D) of Connecticut turned back the challenge of her lieutenant governor, Democrat Robert K. Killian yesterday as voters in 14 states and the District of Columbia went to the polls in the busiest primary day of 1978.

Grasso took a 5-to-2 lead over Killian, her 1974 running mate, as returns piled up from 107 to 169 towns. Killian, who had complained that he was "shut out" by the state's first woman governor, was expected to narrow the margin in returns from Hartford and other major cities, but Grasso's lead was insurmountable.

In New Hampshire, Sen. Thomas McIntyre (D) easily overcame the challenge of Raymond Coughlan, a retired naval engineer. Gov. Meldrim Thomson (R) had a big lead in early returns on the gubernatorial race.

Yesterday's balloting determined the nominations for 12 governorships, six Senate seats and 100 seats in the House of Representatives.

Three other Democratic governors - Hugh L. Carey of New York, Martin Schreiber of Wisconsin and Blair Lee of Maryland - faced serious challenges for renomination. Otherwise, most congressional and gubernatorial incumbents seeking reelection this year seemed to have little to worry about from yesterday's elections.

Voting was generally reported light, but in Minnesota, where two Senate seats and the governorship were up, voters waited in long lines under stormy skies to cast their ballots.

State-by-state summaries:

NEW YORK - Gov. Carey, who won his job by a big margin four years ago, faced strong challenges from two of his former supporters - Mary Ann Krupsak, Carey's lieutenant governor, and state Sen. Jeremiah Bloom, from Carey's home district in Brooklyn. Late polls predicted that Carey would win the primary by a healthy margin.

Rep. Frederick Richmond, a Brooklyn Democrat, had a close primary challenge from Bernard Gifford, who reminded the voters that Richmond pleaded guilty last spring to making a sexual advance toward a male teenager.

RHODE ISLAND - The Democratic senatorial primary had been called a war between a battleship and two rowboats. Sen. Claiborne Pell, the battleship of that analogy, seemed to be a shoo-in for renomination.

The Republican mayor of Providence, Vincent Cianci, faced a primary challenge and may have had difficulty because of an article in New Times magazine that alleged that the mayor was accused of rape in 1966.

VERMONT - Republican Gov. Richard Snelling and Rep. James Jeffords were unopposed for renomination. There were contests for both jobs on the Democratic ballot, although the right to challenge either Snelling or Jeffords is a dubious privilege.

NEW HAMPSHIRE - Gov. Meldrim Thomson Jr., a Republican, and Sen. Thomas McIntyre, a Democrat, were expected to win renomination. Thomson's GOP opponent, former governor Wesley Powell, has threatened to run this fall as an independent if Thomson were nominated again.

FLORIDA - Seven Democrats were in a tight scramble in a race to succeed retiring Gov. Reubin Askew that was almost certain to go into a runoff Oct. 10. Jack Eckerd, 65, was favored over state Rep. Lou Frey (R-Winter Park) in the Republican primary. Two congressmen, Democrat Sam Gibbons and Republican Herbert Burke, faced spirited primary challenges.

NEVADA - Three Republicans and seven Democrats were battling for the right to succeed retiring Gov. Mike O'Callaghan. Attorney General Robert List was favored on the Republican side. Lt. Gov. Robert Rose was favored on the Democratic side.