Aboulaye Gueye added a career-high 14 points for Tech (8-7).
The game was tight through the first half as the Yellow Jackets rode a 7-0 closing run for a 37-33 halftime advantage.
Miye Oni scored 10 of his 14 points before intermission for Yale (7-9), but Tech limited him to 2-of-7 shooting in the second half. Paul Atkinson added 10 points for the Bulldogs, who were outrebounded 34-23 by the bigger Jackets.
Yale, which last led 33-30 on Atkinson's 3-point play with 2:53 to go, made 6 of 15 3-pointers before halftime and just 3 of 12 afterward.
The Jackets expanded the lead to 55-42 when Alvarado took off on a fast break, and just as he entered the lane, bounced a pass backward between his legs to Okogie, who dunked with 13:38 remaining.
Yale missed senior guard Makai Mason, who is out for the season with a foot injury suffered in the preseason. He led the Bulldogs to an upset of Baylor in the 2016 NCAA Tournament and then missed last season with a foot injury. He is expected to graduate in May and play one season for Baylor because the Ivy League does not allow redshirt years so as to afford a fifth-year of eligibility for student-athletes.
Georgia Tech has been wracked by injuries and other absences, but the Jackets are rounding into form. Freshman guard Curtis Haywood played for the first time Saturday after missing six games with a right shin injury. He played nine minutes without taking a shot. Forward Sylvester Ogbonda (ankle) also played for the first time in six weeks.
Yale will kick off Ivy League play Friday against Brown before a rematch at Brown one week later.
Georgia Tech returns to Atlantic Coast Conference action with a Wednesday rematch at home against Notre Dame. The Fighting Irish beat the visiting Yellow Jackets 68-59 on Dec. 30 in the league opener for both teams.