We were elated to learn that our class had won the Cleanest Class Award.
Would it also be correct if I used "won'" in place of 'had won'?
I agree with bhaisahib completely, but have to admit that the simple past is often heard in place of the past perfect in AmE. In my opinion, most native speakers of AmE no longer get the point of the past perfect tense.
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To me it seems incomplete/wrong without "had".