Scrum-half Richie Rees, full-back Michael Horak and number eight Juan Manuel Leguizamon all scored tries as the Exiles led 19-12 at half-time.
Rees' second try extended the lead on the resumption, then Rikki Flutey grabbed another before Saracens prop Ben Broster was sin-binned with 15 minutes left.
Barry Everitt kicked a penalty to see the Exiles home.
|"We've got a couple of talented young kids in the academy but it's a big ask to get those guys to step up."|
London Irish director of Brian Smith praised the home side's performance.
"We played some really good rugby. We turned it over a little bit in the first 20 minutes but we played some cracking stuff.
"Against Bristol for 40 minutes we were our old selves, then for 40 minutes we made some silly decisions. It's nice to put a decent 80 minutes together.
"We had a setback early on with Neal Hatley coming off injured, but I thought we had the better of them at scrum time as well.
"We've got a couple of talented young kids in the academy but it's a big ask to get those guys to step up to this stage [and replace Hatley]. We'll continue to bandage the blokes together and ask them to do the best they can."