The Oak Leafers were denied a quarter-final meeting with Kerry as Conor Sweeney's two late points put Tipp into the last eight for the first time.
Mark Lynch scored a fine goal as Derry led 1-8 to 0-10 at half-time.
Kevin O'Halloran netted for Tipperary while Eoghan Brown got Derry's second goal to edge them into a narrow lead.
But Tipperary, better known as a hurling county, never gave up and got the stoppage-time points to earn a quarter-final meeting against Galway.
Derry had staged late comebacks to win in previous rounds against Louth, Meath and Cavan - but fell agonisingly short on this occasion.
They were outscored for most of the first half but Lynch's first-time shot into the net from Danny Heavron's lay-off gave them a huge boost.
But a mistake by Derry goalkeeper Thomas Mallon in the 48th minute was the big moment in what was an entertaining game.
Mallon slid as he kicked out, and the ball went straight to O'Halloran who advanced to find the net.
Three Michael Quinlivan frees and points by Josh Keane and sub Bill Maher had outsiders Tipp 1-18 to 1-13 up on 60 minutes.
Derry mounted a brilliant rally with Emmett Bradley, Heavron, Lynch, McGoldrick and Christopher Bradley all scoring.
Then came Brown's close-range goal from Ciaran McFaul's pass which edged Derry ahead.
The impressive Heavron added a point before having to off with cramp.
But it was not enough as Sweeney scored the points in time added on to end Derry's Championship season.
Saturday 23 July
All-Ireland SFC Qualifiers Round 4A
Clare 2-12 1-9 Roscommon
Derry 2-17 1-21 Tipperary
Derry suffered a one-point defeat in the fourth round of the All-Ireland qualifiers as Tipperary snatched a stoppage-time win at Breffni Park.