First five Danny Cipriani, lock Dave Attwood, No 8 Nick Easter, flanker Calum Clark, prop Alex Corbisiero and hooker Luke Cowan-Dickie also missed out.
Burgess's inclusion caps a remarkable rise after he switched from rugby league at the start of the year and spent much of his early time in union playing as a flanker.
Lancaster, however, has been hugely impressed by his physicality and big-match temperament and, after just over one hour's international action in the home warm-up against France, has trusted him to continue his progress in the white heat of a World Cup.
"Sam has done great," Lancaster said.
"I wouldn't describe it as a gamble. I understand the size of this decision, but I understand the size of every selection. I trust both him and Henry from what we've seen in camp. The impact they made on their debuts was impressive."
Slade made his debut alongside Burgess at Twickenham earlier this month and offers a classy, creative alternative in midfield and also covers first five.
Jonathan Joseph and Brad Barritt are the other midfielders, leaving Burrell, a regular in the last two Six Nations, to make way.
The inclusion of Slade finally shut the door on Cipriani, who could not oust George Ford or Owen Farrell from the first five berths or Mike Brown or Alex Goode from fullback.
"We felt with Henry and Sam as a duo they really impressed. Henry has been excellent for Exeter and has earned his stripes in the Premiership," Lancaster said.
"Sam's come in from a new code and both of them have absolutely trained the house down. They made two debuts I have not seen before. They've earned their place."
Ben Morgan, who made his first appearance in eight months against France at Twickenham following a broken leg, has seen off the challenge of Nick Easter as No 8 back up to Billy Vunipola.
"With three weeks to go before we play Fiji [in the opening game of the World Cup] we believe we are in good shape as we head into the game against Ireland," Lancaster said of his final warm-up fixture, at Twickenham on September 5.
Squad:
Forwards: Joe Marler, Mako Vunipola, Kieran Brookes, David Wilson, Dan Cole, Tom Youngs, Rob Webber, Jamie George, Geoff Parling, Joe Launchbury, George Kruis, Courtney Lawes, James Haskell, Chris Robshaw (captain), Tom Wood, Billy Vunipola, Ben Morgan.
Backs: Mike Brown, Alex Goode, Jonny May, Jack Nowell, Anthony Watson, Jonathan Joseph, Henry Slade, Brad Barritt, Sam Burgess, Owen Farrell, George Ford, Ben Youngs, Danny Care, Richard Wigglesworth.
