We watched them score one after another.

Literal

We [topic-は] they [subject-が] one-after-another-[adverbial-と] score [nominalizer-の]-[object-を] saw.

The construction [clause]-の-を-見る ('saw that [clause]' / 'saw [clause] happen') is how Japanese expresses direct perception of events. The subordinate clause 彼らが次々と得点する ('they score one after another') is nominalized with の and made the object of 見る. The embedded subject 彼ら is marked with が (not は) because it sits inside a subordinate clause.