Nixon's policy of detente was broadly successful. Tensions between the US and the Soviet Union eased significantly during the early 1970s.
One of the major reasons for this was the fact that Nixon was successful in his efforts to open diplomatic relations with China. By doing this, Nixon put more pressure on the Soviet Union to relax its attitude towards the US. The Soviets had to do this for fear of a US-Chinese alliance that would have endangered Soviet security.
A second reason for this comes not from Nixon but from the Soviet Union. The Soviet leaders during this time were not notable for their hard line attitudes. This made it much more likely that the policy of detente would succeed.