I believe the Velvet revolution in Czechoslovakia matches your criteria. It started with popular protests in November 1989. During December, the (Communist) president nominated a new government where the Communist party held 10 out of 21 seats. Then in June 1990, free elections were held and the Communist party was voted out of power, no longer being part of the government formed based on these elections.

If you consider it sovereign, East Germany did that.

Well, they had already lost almost all control anyways, but after the wall fell they simply ran for the first election with other parties, and - obviously - lost.

So you could say that they were knowingly giving up all their power in the form of an election, but it was an election nonetheless.

In the Republic of San Marino, an elected Communist-Socialist coalition government ruled from 1983 to 1988. They lost their majority when the Socialists scored badly in the 1988 elections, and the government was peacefully replaced by an improbable alliance including communists and christians-democrats.

After 1992's elections, communists left the government, once again without violence.

The Unified Communist Party of Nepal (Maoist) won elections in 2008, and subsequently lost power to the Nepali Congress in the 2013 elections.

The Communist Party of Nepal (Unified Marxist-Leninist) has led four governments in Nepal, the last one losing power to the Nepali Congress in 2016.

The two communist parties merged in 2018, forming the Nepal Communist Party, which is currently in power.

The Economist Intelligence Unit has rated Nepal as a "hybrid regime", so elections may not be fully free and fair.

I think the election to the upper chamber of Polish parliament (Senat) in 1989 can be considered such case.

According to the agreements of the Round Table (Okrągły Stół) the lower chamber (Sejm) had an established number of seats (65%) pre-assigned for the governing communist party (PZPR) and their satellites and the remaining MPs were selected in an entirely free election. All those freely elected MPs but 1 were captured by opposing Solidarity (Solidarność) party. Moreover the leading party decided to take only below 40% of MPs giving the rest of the "contingent" to its satellite parties (my guess is they wanted to show a divergence to cool down the anti-communist movement).

Yet all 100 seats in the upper chamber were selected freely.

As a result 99 of senators came from the main opposing party Soladarity with the remaining one place taken by a politician who was independent (but supporting opposition as well). It was a massive loss, unexpected by either of the sides.

The communists decided to accept those results. Annulling them would most probably lead back to massive unrest, strikes, you name it.

Interestingly the opposition managed to convince the satellite parties of PZPR to switch sides. As a result in August 1989 PZPR lost the majority in Polish parliament lower chamber as well effectively closing the communists rule over the Poland. All the upcoming elections (presidential in 1990 and parliamentary in 1991) were completely free and won by the recent opposition (now divergent, with a number of parties).

See this Wikipedia article as a lead in.

Austria in 1945 had, like most of Eastern Europe, a provisional government which was approved by Stalin and had a large Communist contingent. Unlike other countries, however, the Austrian Communists did not freeze out and later ban all other parties; instead truly free elections were held, which resulted in the Communist Party ceasing to be a part of the governing coalition in 1947. This may have been because the party genuinely thought it would be more popular than the alternatives among voters who remembered Hitler, or it may have been because, Austria having been divided into four Occupation Zones, the Red Army was not the ultimate arbiter.

It's not clear how far this government could claim to be 'sovereign'; but if you are looking for a Communist government that neither seized power by military force nor used the army to retain power once gained (either of which mortgages sovereignty to the military commanders), you will have a long search

The Sandinista government of Nicaragua considered themselves revolutionary Marxists, allied with Cuba and the Soviet Union in the 1980s, and were called Communists by the Reagan administration, which funded an insurgency against them. Their domestic policies were left-wing, but not very similar to the Soviet Union’s.

They lost an election in 1990, had a peaceful transition of power, and the party continued to run in and win elections afterwards.

The Sandinista National Liberation Front (SNLF) or Sandinistas in Nicaragua. They came to power when they overthrew Anastasio Somoza DeBayle in 1979 and then ruled Nicaragua from 1979 to 1990. Then lost the Presidency in an election to Violeta Barrios de Chamorro in 1990. The SNLF's President Daniel Ortega returned to power in 2006 through the electoral process and has since won re-election in 2011 and 2016.

I think Cyprus qualifies here.

Demetris_Christofias was president of Cyprus from 2008 to 2013. He was the candidate of the communist / Marxist-Leninist Progressive Party of Working People and Cyprus is the only EU country which has had a communist head of state.

In Cyprus, the president is both head of state and heads the government. It is not a ceremonial position, the president has real power. His party did not have a majority in parliament but it was the largest party at the time Christofias was elected president. Before becoming president of Cyprus he was president of the house of representative 2001-08 (the Cypriot parliament). He decided not run for reelection in 2013 and the president who was elected after him was not a communist.