"Exporting ideology" was certainly the biggest such success.

The USSR utilized to the best of its ability and with a significant dose of success the "revolutionary movement" throughout the colonies and former colonies of the western powers. The Soviet Union established a special university which catered extensively to third world students who then returned home and spread sympathetic ideology - the People's Friendship University - which educated many of the future revolutionary and anti-colonialist cadres in Africa and Asia. While the west utilized money and political influence to maintain a largely neo-colonial world order the Soviets used political subversion with great success and undermined those efforts with much greater efficiency. The wave of independence movements throughout Africa would not be possible without Soviet help and involvement. The USSR by the virtue of not being bound by profit-focused economic logic exported many rugged and cheap weapons preferred by the Soviets to third world countries. The most easily recognizable example is the AK-47 which became the most widely used automatic rifle in history. There is a reason why it is on a flag of Mozambique. The Soviet Union also mass-produced the most widely used tank in history - the T-54/55 family which is used even today by many countries around the world.

Arguably the western bloc has been far less successful in this field and with the exception of the European satellite states which considered themselves occupied by the USSR to begin with it took some time after USSR collapsed to gain a foothold in those former Soviet-friendly countries. Soviet involvement in the revolutionary movements in Latin America caused the US to support some of the most brutal dictatorships which have been seen not as desirable but as the only guarantee that the inequality-ridden societies of this region would not turn into new socialist or Soviet-friendly states like Cuba. The main advantage the US had during the Cold War was fighting away from home and Cuban revolution was a warning call that the potential fronline might come very close at any time if they are not careful.

There are some minor achievements, especially in the field of military technology which are quite impressive considering Soviet Union's economic disadvantage but I don't think they could be listed as "things Ivan did better" since they have been achieved at a staggering cost to the general economy and hampered ordinary people's standard of living. The process of "exporting ideology" was an exception to this rule which we must remember came at an advantageous time when the US was taking over the role of the global hegemon from Britain and France, thus inheriting the job of providing peace and stability throughout huge colonial empires while not being too fond of colonial ideology itself.

For example many people think of the US as a fervent supporter of expansionist Israeli policies but in truth the first and most staunch supporters of strong and independent Israel were both Britain and France, colonial powers hoping to preserve influence in the region with the help of the fledgling state while the US was much more reserved and cautious. It wasn't until the US took over in the aftermath of the Suez Crisis and the 1956 war and became finally embroiled in playing the regional peacekeeper that the USSR decided it needed to balance the powers and became engaged on the side of the Arab states - Syria in particular - even though until 1967 the former Jewish emigrees from the USSR were among the most influential elements in early Israeli society and the USSR was one of the staunchest supporters of the creation of Israel immediately after WW2.

Also let's not forget that the domestic issue of racial inequality was a serious problem in trying to implement anti-Soviet agenda in Africa. US involvement in Vietnam - very unfortunate and ill-thought - guaranteed that US would have a handicap when dealing in South-East Asia. The refusal to back India against Pakistan in 1971 in - as some suggest - a show of solidarity with post-colonial British interest also pushed the relatively pro-western India towards the USSR, a relationship which lasted well beyond the collapse of the Soviet Union and which only in the recent years is showing signs of change.

EDIT:

Per request. This is a very general explanation of the use of "revolutionary warfare" which I recanted from memory so I can't really pin-point any specific source. Here are some English-language publications on the topic which should cover it in greater detail.

R. Staar - Foreign Policies of the Soviet Union
R. Schultz - Soviet Union and Revolutionary Warfare
I. Natufe - Soviet Policy in Africa - From Lenin to Brezhnev

A declassified CIA report on Soviet involvement in Latin America.