Missing oil seals apparently caused the failure of all three engines on an Eastern Airlines jumbo jet carrying 172 people between Miami and Nassau yesterday, but the pilot was able to restart one engine and make a safe emergency landing in Miami.

Passengers put on their life vests and Coast Guard cutters moved into position as the jetliner fell powerless over the Caribbean from 23,000 feet to 2,800 feet--almost four miles--before the crew regained control with one crippled but functioning engine.

"We were close to death," Parisian Phillippe Sostre told the Associated Press. "I am now very tired. This was the first time we flew with an American airline and the last."

All but 48 of the 162 passengers took a later flight to Nassau after Eastern broke out the liquor for them in Miami.

"Everybody was pretty happy when they left the second time," an airline official said. "I didn't even get a drink, and I could use one."

Jim Ashlock, an Eastern spokesman, said that O-rings--gaskets or washers that seal against an oil leak--were missing from each of the three engines when they were inspected after the incident. "I don't know why," he said.

The O-rings seal a 5/8-inch bolt that penetrates the oil system in the huge Rolls Royce RB211 jet engines on the Lockheed L1011, federal officials said. The bolt is magnetized to capture metal chips, and it must be withdrawn and inspected every 30 hours of aircraft operation--a two- to four-day cycle. Ashlock said he did not know when, where or by which mechanics the bolts were last inspected.

The high-frequency oil inspections were ordered recently by the Federal Aviation Administration after the RB211s began to develop bearing problems. Metal chips in the oil are an early sign of difficulty with the bearing, federal officials said. The oil system on each engine is independent of the other two engines; each engine has its own inspection bolt.

National Transportation Safety Board and Federal Aviation Administration officials started investigations yesterday.

A spokesman for the transportation board refused to pin the blame for the missing O-rings, saying, "We have yet to determine whether the plugs are supposed to come out of the stock room with the O-ring or whether the mechanics are supposed to put the O-ring on."

An Eastern mechanic, who spoke on condition he not be identified, told the Associated Press that the rings are sometimes put onto the plugs by workers in the stock room, and sometimes by the mechanics. But he said that in either case it is the mechanics' job to check to make sure the rings are in place before the plugs are re-installed in the engines.

The incident occurred on Eastern Flight 855, which left Miami about 8:55 a.m. and climbed to 23,000 feet for the one-hour flight to Nassau. Just as the flight was about to begin its descent, an indicator light in the cockpit showed low oil pressure in the center engine. Capt. R.E. Boddy immediately shut down that engine and turned back to Miami, although he apparently was closer to Nassau. That was a routine procedure, Ashlock said, because the L1011--and other jumbos--should be able to fly without difficulty with one engine out. Miami is Eastern's maintenance base.

However, the plane's left- and right-wing engines also began to develop oil problems and, federal sources said, eventually seized. The captain was then able to restart the center engine he had shut down. Aviation experts suggested that the captain may well have saved the flight by shutting down the center engine at the first sign of trouble and thus preserving its oil. Oil is used to lubricate moving parts in a jet engine just as it is in an automobile engine.

Passengers interviewed in Miami said the captain kept them advised of how serious their situation was during the 10-minute plunge. Many of them took new interest in the seat-pocket safety cards that tell how to evacuate a plane and inflate the life rafts.

Passenger Tom Nolan quoted the captain as saying "Be ready to open the doors and hit the water."

"When he said that, I don't think I ever heard a worse phrase in my life," said Dr. Bruce Jacobs, a dentist from Hollywood, Fla.

Passenger Rosemarie Zuppardo of New Orleans summed up the passengers' reaction to their safe landing in two words: "Thank God!"

And Betsy Davis put it another way: "Air travel will never be the same."