Sean Rodriguez started in place of Longoria at third, while Justin Ruggiano replaced Upton in center field.
"We have a little bit of a bug among us," Rays manager Joe Maddon said. "Other guys have had a little bit of an issue, as well."
While both Longoria and Upton wanted to play, Maddon felt more comfortable having them rest and used as pinch-hitters, if necessary.
Maddon believes the ailment should last no longer than 24 to 48 hours.
"I looked at Upton and thought it would be best to get him well by the middle of tonight's game, so we can use him later in the game if we have to," Maddon said.
"He had that look about him that wasn't very strong. Longoria had some of the same issues."
Monday's rest may help Upton get out of his current funk at the plate. In his last 10 games, Upton is batting just .094 (3-for-32) with one RBI and 13 strikeouts.
Longoria, a late scratch from the lineup, hoped to be back in the starting lineup after leaving Saturday's game against the Seattle Mariners with tightness in his left side.
Enjoying the friendly confines of Angel Stadium, Longoria has a career .413 average, his highest average at any American League ballpark. He also has four home runs, 13 RBIs and nine doubles in 46 career at-bats.