To win after hard bidding (to outbid others); by extension, to eke out a victory in a close contest.
彼は激しい入札の末、アンティークの椅子を競り勝った。
After intense bidding, he outbid others and won the antique chair.
うちは他社を競り勝ってその土地を手に入れた。
We outbid other companies and acquired the land.
チームは接戦を競り勝って決勝へ進んだ。
The team narrowly won the close match and advanced to the finals.