That in turn means that they have a trip to London Wasps on Saturday, May 17, to book their place in the Twickenham Final against regular season winners Gloucester.
On the day, Saints scored three tries, meaning that their ascension into third spot was due to their superior 'games won' tally over Sharks, as the two were tied on points.
Saints had won only one more game than Sharks, but that was enough to send them into the semi-final, courtesy of a late rally.
Hooker Steve Thompson and Spanish wing Oriol Ripol scored tries in the last five minutes, adding to Australian centre Peter Jorgensen's earlier effort, in his last home match for the club.
Kiwi Bruce Reihana assumed kicking duties, adding two penalties and a conversion, with Jorgensen also striking a conversion, after Paul Grayson had struck an early drop-goal to get them up and running.
Losers Leeds only managed two Braam van Straaten penalties early on, and end the season in fifth place, facing a Zurich Wildcard match at home against Saracens on Sunday May 18 to keep their Heineken Cup dream alive.
For Northampton Saints:Tries: Jorgensen, Thompson, RipolCons: Reihana, JorgensenPens: Reihana 2DG: Grayson
For Leeds Tykes:Pens: Van Straaten 2