Murphy and Tuilagi were both absent from the comfortable victory over Worcester Warriors at Sixways on Tuesday but come back into the starting XV for Sunday's contest.
With Manu Tuilagi missing due to a hamstring injury, Matt Smith moves from wing to centre while full-back Scott Hamilton drops to the bench.
Up front Martin Castrogiovanni and Rob Hawkins, who started the Warriors game on the bench, are both given starts while Graham Kitchener replaces the injured Louis Deacon at lock.
Steve Mafi and Julian Salvi return to the back row alongside Thomas Waldrom.
"We've had a very short turnaround from Tuesday so we're managing all of the squad through this period," director of rugby Richard Cockerill told the Tigers' official website.
"This is a very important game for us, especially with another home game to follow against Wasps next weekend.
"Sale have had a good start to the season, they are above us in the Aviva Premiership table and Steve Diamond has done a good job in a very short period of time there."
Meanwhile, Sale have made two changes to the side that beat Newcastle 27-19 on Boxing Day.
Joaquin Tuculet comes in for England international Mark Cueto on the left wing, with Tony Buckley taking over from Henry Thomas at prop.
"It's a massive challenge for us to go to Welford Road, but players and coaches are involved in the game for the chance to visit stadia like that, with a full house, on New Year's Day and put up a performance," Sharks' executive director of sport Steve Diamond told the team's official website.
"The Leicester crowd is knowledgeable and we hope to show them something to applaud."
Leicester: 15 Geordan Murphy (capt), 14 Horacio Agulla, 13 Matt Smith, 12 Billy Twelvetrees, 11 Alesana Tuilagi, 10 Toby Flood, 9 Ben Youngs, 8 Thomas Waldrom, 7 Julian Salvi, 6 Steve Mafi, 5 Graham Kitchener, 4 Ed Slater, 3 Dan Cole, 2 Rob Hawkins, 1 Martin Castrogiovanni.
Replacements:16 George Chuter, 17 Boris Stankovich, 18 Logoviii Mulipola, 19 Ben Woods, 20 Tom Croft, 21 Micky Young, 22 Jeremy Staunton, 23 Scott Hamilton.
Sale: 15 Rob Miller, 14 Tom Brady, 13 Johnny Leota, 12 Sam Tuitupou (capt), 11 Joaquin Tuculet, 10 Nick Macleod, 9 Dwayne Peel, 8 Andy Powell, 7 David Seymour, 6 James Gaskell, 5 Andrei Ostrikov, 4 Fraser McKenzie, 3 Tony Buckley, 2 Marc Jones, 1 Alasdair Dickinson.
Replacements: 16 Andy Titterrell, 17 Vadim Cobilas, 18 Henry Thomas, 19 Kearnan Myall, 20 Mark Easter, 21 Cillian Willis, 22 Andrew Higgins, 23 Will Addison.
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