Tagoe batted a Terrance Ervin pass and Velasquez returned it 39 yards to put the FCS-ranked Tribe (2-1) ahead 14-7 in the first quarter.
In the fourth quarter, DeAndre Houston-Carson blocked a field-goal attempt and Tagoe returned it 66 yards.
The Tribe defense added a safety when Aaron Daniels was tackled in the end zone by Airek Green. Steve Cluley threw a touchdown pass to Tre McBride, who had 101 yards receiving, and John Carpenter added two field goals for the Tribe.
Daniels, who had 106 yards rushing, scored on a 7-yard run to give the Spartans (0-3) their first touchdown of the season and only lead of the game.