Khrushchev had been a part of Stalin's elite club since the 1930s and he had served Stalin's policies until 1953. It seems that during this time he had really been drawn in by Stalin's cult of personality and truly believed in those policies. It wasn't until Stalin's death that we would actually see Khrushchev's anti-Stalinist side come out.

It's true that Molotov did resemble Stalin as an Old Bolshevik, but it seems that he simply never really had the ambition to hold the ultimate position of power during the crucial leadership struggle after Stalin's death. He was content being given the Minister of Foreign Affairs position back to him in 1953 and didn't get himself too involved in the mess that came in the following years.

Molotov was part of the failed coup to remove Khrushchev in 1957 though, in which he was designed to replace Khrushchev as the First Secretary. He was certainly unhappy with Khrushchev's policies at that point and thought Khrushchev had gone too far in condemning Stalin in 1956. But Khrushchev managed to hold on to power and expelled Molotov to Mongolia, where the latter became USSR's ambassador.

When Stalin died in 1953, there were no rules on how to choose the next leader of the USSR and Stalin had ensured that there was no natural successor that was an obvious choice either. The structure of the top USSR leadership was not very straightforward and the Communist Party had to figure out whether it was the USSR Council of Ministers or the Party Presidium that should be the more important institution of the two. But there were four men who did seem to want to become the next Stalin—Malenkov, Beria, Bulganin, and Khrushchev. Here's what happened to the four of them.

Beria was actually very close to resembling Stalin's leadership style. He was in charge of the NKVD under Stalin and in 1953 in charge of the Ministry of Foreign Affairs (MVD). He had much of the police and much of the military on his side (his men guarded the nuclear bombs for example). He also was a master of governing through secrecy and fear, a trait he perfected under Stalin.

Khrushchev was deeply afraid of Beria and of the idea that Beria might become the next Soviet leader. So through some political maneuvering, Khrushchev organized a conspiracy against Beria. Bulganin was nominated to be the Secretary of Defence in 1953 by Khrushchev and joined his side with the military that Beria did not hold at that point. Malenkov joined the conspiracy when he realized that Beria was being politically outmaneuvered.

By handing several top military leadership spots to loyal supporters, Khrushchev managed to get around Beria's MVD support. Beria was arrested, tried, and executed for being the enemy of the Party and the people. After his execution, the remaining trio shared power at the top of the Soviet government together.

Khrushchev became First Secretary (leader of the party) in 1953, which did not give him the outright top leadership position. But because being First Secretary gave him the power to appoint a wide array of key government officials, Khrushchev used it to build up a strong group of supporters within. For example, after Beria's fall, some of the MVD's responsibilities became the responsibilities of the newly formed KGB. Khrushchev was able to appoint his own supporter to become the new chief of the KGB in 1954.

Malenkov had been the Premier of the USSR (the prime minister) from 1953 to 1955 when he was forced to resign. He failed to get the same kind of supporters inside the government like Khrushchev did because he had tried to appeal to the citizens rather than officials and his policies as Premier were slow to adapt to reform. He was accused of being tied to Baria and had lost out in the power struggle against Khrushchev.

Bulganin replaced Malenkov as the Premier in 1955 and supported Khrushchev at first. He oversaw some destalinization but had become not happy with Khrushchev's policies a couple of years after. He joined Molotov and Malenkov in the attempt to push Khrushchev out of power in 1957. However, since that coup failed, Bulganin's status had drastically diminished. He stayed as the Premier for another year, but after the coup Khrushchev had really solidified his grasp on the leadership of the party to where Bulganin was just a figurehead.

So by 1957, Khrushchev had become both the First Secretary, a position he had held since 1953, and replaced Bulganin as the Premier (officially not until 1958, but Khruschev held the power of that office after the coup). By establishing himself in power of the highest two leadership positions in the Soviet government he finally gained sole control over the USSR. He was left as the sole remaining figure of the four that wanted that power after Stalin's death.

Source:

The Khrushchev Era 1953-1964 by Martin McCauley.