Tipsarevic, who is back after missing much of the past two seasons with hamstring issues, beat Sandgren 6-1, 7-6 (4).
Sam Querrey, a two-time finalist, began the tournament with a 6-3, 6-4 win over Bjorn Fratangelo.
In other first-round action, Henri Laaksonen defeated Mackenzie McDonald 6-3, 6-4, Jordan Thompson beat Pedja Krstin 7-5, 6-2, Santiago Giraldo defeated Bradley Klahn 6-4, 6-4, Daniel Elahi Galan beat Paolo Lorenzi 7-6 (5), 6-4 and Guillermo Garcia-Lopez defeated Noah Rubin 6(5)-7, 6-3, 6-3.
Taylor Fritz and Reilly Opelka defeated Luke Bambridge and Jonny O'Mara 6-3, 6-4 in the first round of doubles play.
Other doubles action included Jeremy Chardy and Fabrice Martin's 7-5, 6-3 win over Pablo Cuevas and Hugo Dellien and Ryan Harrison and Mackenzie McDonald's 4-6, 6-4, 10-2 victory over Marcelo Arevalo and Jamie Cerretani.
Play continues with the second round on Wednesday.