pulled it off, as defined by The Free Dictionary:
pull off something also pull something off: to succeed in doing
something difficult or unexpected.
Examples given by TFD:
He won five straight games and pulled off one of the tournament's
I don't know how you pulled it off, but we're now $5,000 richer than
we were yesterday.
In the OP's example:
The team pulled it off in the final game and won the championship.
By coincidence, the Washington Post used the phrase today (09/22/17) in a story about Sen. McConnell's new drive for ACA [Obamacare] repeal:
By the middle of next week, McConnell might pull off the victory
for Strange [who is running for the seat vacated by Sessions when he
became Attorney General] and have the votes lined up to pass the ACA
repeal, which would his best week as leader since Trump took office.