Tompkins, who delivered a try-scoring debut off the bench when Wales beat Italy 42-0 five days ago, partners Hadleigh Parkes in midfield.
George North, a centre starter against the Azzurri, moves back to his familiar wing position, replacing Johnny McNicholl.
Wales head coach Wayne Pivac has made no other changes to the starting line-up.
Switches among the replacements, though, see McNicholl being joined by prop Rhys Carre, who is available again after serving a suspension following his sending off in Saracens' Champions Cup victory over the Ospreys last month.
Scrum-half Gareth Davies and Gloucester back Owen Williams are also on the bench, together with Ospreys lock Adam Beard, who replaces an injured Cory Hill.
Pivac said: "Nick comes into the side, I thought he played exceptionally well when he came on last week, so he deserves the start.
"We've been seeing it in training every day and the way he conducts himself off the field. He is a true professional. He handles himself very well. He is very impressive.
"We were happy with Johnny (McNicholl). But we just felt we couldn't leave Nick out. It's an opportunity for George on the wing.
"Overall, we got what we wanted out of the Italy game – five points, and there was some good play there and some parts of our game needed to be looked at, which we've done this week.
"Hopefully, there will be a marked improvement, so we got what we needed out of the game and now we move forward, keeping that nucleus as it is to help us achieve that.
"Momentum is important in the championship. It was nice to get a good winning start under our belts, and hopefully we can build on that through the tournament."