The Senate yesterday approved Transportation Secretary Elizabeth Hanford Dole's plan to sell federally owned Conrail to Norfolk Southern Corp. for $1.2 billion and thus create the nation's largest railroad.

The solid administration victory has been expected for months, but the proposal was held up by the Senate's proclivity for delay. The plan now faces an uncertain future in the House.

"This is a giant step forward and a major victory for the American taxpayer," Dole said of the 54-to-39 vote.

Norfolk Southern Chairman Robert B. Claytor -- who sometimes has had difficulty convincing his board that it needed Conrail enough to put up with the immense difficulties of getting a sale through Congress -- was beaming. "I think we have a reasonably good chance in the House," he said.

Dole's proposal survived attacks in the Senate on the grounds that a merger of Conrail and Norfolk Southern would be anticompetitive and that Norfolk Southern is paying too little and would reap too great a tax advantage because of credits it would get through acquisition.

The counterarguments, presented by Dole to many senators and repeated on the floor by Sen. John C. Danforth (R-Mo.), the bill's manager, were primarily that:

It is time for the federal government to stop running railroads, something it doesn't do very well.

The Norfolk Southern deal guarantees "strong viable service in the Northeast for decades to come," as Danforth said.

Conrail -- officially Consolidated Rail Corp. -- was a 1976 invention born of desperation after the collapse of the Penn Central and six other northeastern railroads. It consumed $7 billion in federal money before achieving a turnaround beginning in 1982 when it was able to shed all passenger responsibilities, stop paying state taxes, buy out unneeded employes and quickly abandon unwanted track.

Despite its impressive financial performance since then, Dole and other DOT officials have hammered on the theme that, over the long run, Conrail is a freight railroad in a declining region and has a limited future at best. They actively sought another railroad to purchase Conrail and to bring financial stability and long-term commitment to transportation.

Merged with mighty Norfolk Southern, they argued, Conrail would become an asset, extending Norfolk Southern's single-line routes and markets into the Northeast, where it was shut out, and giving Conrail customers single-train access to the South and Midwest.

The combined railroad would have more than 30,000 miles of track stretching from Boston and Montreal in the east to New Orleans and Jacksonville, Fla., in the south, and St. Louis, Kansas City and Chicago in the west.

It also would be a strong competitor for CSX Corp., the other huge Eastern railroad. CSX bitterly opposed the Norfolk Southern sale, as it promised Dole it would. As the Senate voted yesterday, a row of CSX lobbyists sat in the gallery four rows behind a row of Norfolk Southern lobbyists.

By endorsing Norfolk Southern, the Senate also explicitly rejected an alternative bid of $1.4 billion by a group 43 investors including CSX organized by Morgan Stanley & Co. The investors would sell Conrail to the public over a period of years and permit it to remain as a single entity.

Conrail's management, anxious to continue its profit-producing performance as an independent entity, jumped on the Morgan Stanley bandwagon, joining the senators from Pennsylvania and Ohio, where there is considerable Conrail employment and service.

Sen. Arlen Specter (R-Pa.) urged his colleagues to vote against Norfolk Southern "so there may be significant votes in this body to encourage the fight in the House. . . . We have just begun to fight."

Sen. Howard M. Metzenbaum (D-Ohio) led the procedural fight in the Senate. He was overwhelmed yesterday, by 70 to 17, on the one delaying vote he demanded before the legislation was called. "It will be tough for Norfolk Southern when they go to the House," he predicted.

Thomas A. Saunders III, a Morgan Stanley managing partner, said, "We believe the support our proposal obtained is concrete and tangible evidence of its merits." Its merits are such that, if the House pays attention, "An independent Conrail is assured," Conrail said in its own statement.

An offer of $1.6 billion has been made by a group led by First Boston Corp. and Allen & Co. of New York. There was little, if any, mention of it in two weeks of Senate debate.

At least two, and possibly three, House committees will have a role, with the lead assigned to the Energy and Commerce Committee. The Ways and Means Committee has claimed some jurisdiction because of tax provisions in the legislation, and the Judiciary Committee is interested because of railroad antitrust issues.

However, such matters traditionally reside with Energy and Commerce. Rep. John D. Dingell (D-Mich.), the committee chairman, has been actively seeking information from the Transportation and Justice departments on how Norfolk Southern was selected and how it was decided that a merger with Conrail would not be anticompetitive.

Part of Dingell's inquiry has centered on Justice Department assertions that Norfolk Southern's planned divestitures of track or track-use rights to other railroads appear to solve antitrust concerns.

Dingell has sought all Justice documents and drafts on the subject. Yesterday, he released a memorandum from Justice claiming that a misunderstanding had resulted in the destruction of "both hard copies and the electronic version of the superceded drafts of some correspondence."

Dingell "is interested to see the Conrail sale issue addressed this year, and not to let it die by default," a staffer said. However, Dingell has not announced a position and, to get a decision, he may have to spar with Rep. James J. Florio (D-N.J.), chairman of Energy and Commerce's transportation subcommittee. Florio's enthusiasm for any Conrail sale has long been suspect.