The Justice Department filed a civil antitrust suit yesterday seeking to prevent United Technologies Corp. from acquiring control of Carrier Corp., a leading manufacturer of heating and air conditioning equipment.

The suit, filed in United States District Court in Syracuse, N.Y., charged that the acquisition would violate Section 7 of the Clayton Act. The court was asked to issue a preliminary injunction barring United Technologies from acquiring Carrier stock pending the outcome of the suit.

Justice's action came just days after the State of New York gave United Technologies the go-ahead to proceed with its tender offer by lifting what appeared to be the last of the various governmental restrictions that had blocked it temporarily.

Just before the suit was filed, in fact, United had announced it was commencing its offer to buy up to 17 million shares of Carrier's common stock at $28 a share. In a statement released after the suit was filed, United said it continued to feel its planned acquisition was "lawful" but wasn't surprised by the Justice action.

"It fits in with the philosophy enunciated recently by the Justice Department that it is interested in testing the limits of the antitrust law and will attack any major acquisition or merger," the company said.

Carrier, which has been resisting United's takeover bid since it was announced seven weeks ago and has filed its own suits, yesterday said in a corporation statement that it was "delighted" with the federal government's involvement.

"The department has clearly reached the same conclusion as we have that the merger is illegal because it violates antitrust laws," Carrier said. "Having the Justice Department in the case should help us defeat the takeover."

The government suit contends that the proposed acquisition would hamper competition both in the manufacture and sale of unitary and applied heating and air conditioning systems by entrenching Carrier, and in the development and production of the control devices used to operate those systems.

According to the suit, Carrier is the nation's leading manufacturer of "unitary" heating and air conditioning systems with about twice the sales of its closest competitor. Unitary systems are sold in a single pagage or matched set of components primarily for residences or small commercial establishments.

The unitary market is relatively concentrated, with the top four producers accounting for about 50 percent of total sales, and is characterized by significant barriers to entry, Justice said.

According to the suit, Carrier is also the recognized market leader in the manufacture and sale of "applied" heating and air conditioning systems, more complicated systems requiring that several components for larger buildings are tailored for the structure and assembled at the construction site.

Carrier accounted for about 45 percent of the $220 million worth of applied systems sold in the U.S in 1977, Justice said. That market is highly concentrated, with three producers accounting for 90 percent of the systems sold, and there are significant barriers to entry, the suit contends.

As the marker leader in the applied an unitary systems industry, Carrier is a significant factor in the development and production of control devices for those systems, the suit contends. Carrier also is a substantial purchaser of the devices, buying more than $30 million worth a year. Justice said about $4.5 million in devices was purchased last year from United, which is significant developer, manufacturer and seller of the device through its various subsidiaries and divisions.

United would be eliminated as an independent source of control device and diagonstic technology for other manufacturers, the suit contends.

Combining the two companies would produce the 22d largest domestic industrial corporation ranked by sales and the 41st largest if ranked by total assets.

In a second count, the suit charged that the proposed acquisition would create a market structure conducive to reciprocal dealing by combining a major purchaser of electric motors which require magnetic wire in their construction (Carrier buys about $71.5 million each year) with a major seller of magnet wire (United).