Harvard then took four singles matches, and could have swept had not Green and Lingman lost their singles matches in third set tiebreakers.
The 5-2 victory set up Monday's final against Columbia, which had rolled over Fairleigh-Dickinson, Penn and Princeton in the first three rounds.
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"This means a lot," Green said. "After we lost a lot of players last year, the other Ivy teams were talking about how we would lose and go down. This shows we haven't, even with the young guys."
With the weekend's championship, Harvard earned an automatic berth into the ITA/USTA National Team Indoor Tournament, February 24-27, in Louisville, Kentucky.