Venters, who will be appearing in his 245th game, returned to the majors in April after five years and multiple Tommy John surgeries. He's 1-0 with a 0.87 ERA in 14 games and recently picked up his first save since 2011 when he closed out a victory over Oakland.
"It's been a while, but there's always a certain level of excitement when you get that last out," Venters told ESPN. "I was glad I was able to get it done."
He is slated to go one or two innings before yielding to Ryan Yarbrough as the Rays continue using relief pitchers to begin games.
Venters and Nationals starter Tanner Roark (2-6, 3.61 ERA) will be trying to follow Max Scherzer's latest gem.
Scherzer pitched eight strong innings to become the majors' first 10-game winner in Washington's 4-2 victory Tuesday night. He struck out 13 while scattering five hits and did not allow a runner past second base until pinch hitter Brad Miller's two-out, two-run double in the eighth.
"Twenty-five out of 28 first-pitch strikes," Washington manager Dave Martinez said of Scherzer's effort. "That's pretty much as good as it gets. He was awesome tonight."
Scherzer struck out Johnny Field, Christian Arroyo and Daniel Robertson on a combined nine pitches in the sixth inning. It was the third nine pitch/three strikeout inning in Nationals history and the first since Scherzer did it against Philadelphia on May 14, 2017.
"I honestly didn't know I had it, then I walked off the field and I was like, 'Wait a second, I think that was it,'" said Scherzer, who joined Lefty Grove, Randy Johnson, Sandy Koufax and Nolan Ryan as the only pitchers to accomplish the feat twice.
Matt Adams hit his 13th homer for Washington.
Tampa Bay's Nathan Eovaldi (1-1) gave up four runs in five innings in his second start back from Tommy John surgery.
"I feel like I was ahead in most of the counts tonight," Eovaldi said. "I just couldn't put them away. I just couldn't get that splitter going and the cutter wasn't as good as it was in that opening start."
Roark, who will be making his 12th start of the season, retired one of three hitters and allowed a two-run, walk-off homer in the ninth inning Sunday to take the loss against the Atlanta Braves in his first relief outing of the season.
The Nationals lost starter Jeremy Hellickson in the first inning, so Roark came on with the game tied in the bottom of the ninth. He yielded a double to Dansby Swanson before Charlie Culberson ended it.
Roark has pitched at least seven innings in three of his last four starts and has not allowed a homer in any of them but hasn't won since April 30.
Roark has made one start versus the Rays, allowing one run in seven innings of a 16-4 victory June 16, 2015.
On Tuesday, the Rays put right-hander Chris Archer (left abdominal strain) on the 10-day disabled list. The Nationals put right-hander Hellickson on the 10-day DL with a hamstring strain.
Martinez said second basemen Daniel Murphy will continue his rehab assignment at Double-A Harrisburg. Video of Murphy playing for Harrisburg showed him struggling in the field -- he's made four errors -- and with his running.
"He wants to get comfortable and we thought it was best if he stays down there, keeps getting his at-bats, keeps playing every day until he's ready to come back up here," Martinez said.