Iain Fullarton and Andy Titterrell scored in the 78th and 80th minutes respectively, after the teams were tied at 11-all, to give Sharks a 23-11 win and ensure they stay in touch with the table-topping Gloucester.
It was always going to be a tight affair, but when Michael Horak scored the Exiles' only try after just five minutes it seemed it might be their day.
However, penalties by Charlie Hodgson in the 26th and 40th minutes saw Sale edge ahead 6-5 at the break. They never lost the lead again.
Steve Hanley scored Sale's first try in the 44th minute to open up a gap, before two Mark Mapletoft penalties saw the scores being tied after 71 minutes.
Then came that final burst, in which the Sharks showed how vital it is to keep your concentration for a full 80 minutes.
For London Irish: Try by Michael Horak. Mark Mapletoft kicked two penalties.
For Sale Sharks: Tries by Andy Titterrell, Iain Fullarton and Steven Hanley. Charlie Hodgson kicked one conversion and two penalties.