A hidden partnership for peace in the Middle East has been brought forth by the latest American effort to prevent conflagration in the area. The bedfellows under the blanket are Israel and Saudi Arabia.

They share a joint interest in liniting Soviet influence around their borders. That common goal now finds expression in the crisis that has erupted over Syria's role in Lebanon.

Lebanon is peculiarly suited to bring out the latent harmony between the Israelis and the Saudis. A complicated mosaic of Christian and Moslem communities, it used to furnish financial services to the Arabian peninsula while enjoying relatively good relations with Israel. The Six Day War of 1967 stimulated a massive influx of refugees who identified with the Palestinian resistance. The Palestine Liberation Organization took over a portion of Lebanon as a staging ground for attacks on Israel.

Clashes between the PLO and the Labanese authorities fostered a civil war between the Moslem and Christian communities. Syrian forces intervened to put down the trouble in 1975. Since then, Lebanon has been a confused battleground among the Syrians, the PLO, various Moslem communities and some Christian communities supported by the Israelis.

The most recent trouble broke out when one of the Christian communities started to occupy a town in a valley that runs south toward Israel. Syrian froces mounted air and artillery attacks on the Christians. The Israeli air force shot down two Syrian helicopters. The Syrians then moved into the valley some ground-to-air missiles furnished by the Soviet Union. The Israelis threatened to wipe out the missiles. At that point, Secretary of State Alexander Haig summoned former ambassador Philip Habib out of retirement. Habib has been shuttling back and forth among Lebanon, Syria, Israel and Saudi Arabia ever since.

A striking absence of conflict between Moslems and Christians in Lebanon has marked this latest period of almost constant high tension. After years of strife, the various Lebanese communities now seem prepared to bury the hatchet. So the essence of the proposals advanced by Habib has been a restoration of authority to the Lebanese government and a gradual scaling down of the positions staked out in the country by the Syrians, the Israelis and the Palestinians.

The Russians enter the picture as the chief supporters of the Syrian regime of President Hafez Assad, who has been under pressure at home and increasingly isolated in the Arab world. A top Soviet diplomat, Georgi Kornienko, visited Damascus just after the mussiles were moved forward. As a backup to the Habib mission, Haig has been inviting the Russians, through Ambassador Anatoliy Dobrynin, to exercise a restraining influence in the Syrians.

The Soviet response has been unclear. American officials believe Moscow has assured President Assad of continued support. But they do not think Russia has been needling the crisis, pushing the Syrians on in order to test the reactions of the Reagan administration.

On the contrary, the Washington view, which tended to be confirmed by President Brezhnev's speech Friday, is that the Russians would like to use the occasion as a vehicle for re-entry into Middle East diplomacy. The American hope is to hold the Russians off, while wooing the Syrians away from Moscow by a combined carrot-and-stick approach. Which is where the Israelis and Saudis come in.

Israel holds the stick. Israeli planes could take out the missiles, the Prime Minister Menachem Begin has military reasons, as well as the possibility of political gains in a pre-electoral period, to order a strike. While urging restraint upon the Israeli leader, the United States has not flatly condemned military action. Rather it has tried to use the threat as one reason for the Syrians to remove the missiles.

The Saudis hold the carrot. President Assad cannot be seen yielding to Israeli threats, and he flatly rejected Habib's original plea to pull out the missiles. But if Saudi officials make the plea, and if they accompany it with financial aid and measures that bring Syria back into the Arab community, that is a very different story. Assad can easily accept from the Saudis what he has to spurn when it comes from Israel.

With so many uncertainties in play, the outcome of the Habib mission remains in doubt. But the mission rests on a solid base -- the hidden partnership between Israel and Saudi Arabia that the Reagan administration has had the wit to evoke.