It is true that with the verb "to be" you would need a predicate nominative. This is why we need to use "we." This sounds odd, but it is correct. The reason for this is that "we" is the nominative; "us" is the accusative case, that is the direct object. 

Hence, the sentence should be: "The winners of the cheerleading contest were we, the juniors." If we write the sentence is another way, you will be able to see that this is the correct way to look at it. We can always say: "We, the juniors, were the winners of the cheerleading contest." To use "us" would be wrong. 

Unfortunately, too many people today speak incorrectly when it comes to the nominative verses accusative case.