Armitage, who had been on the bench for the previous two matches, struck in each half for Irish, whose other nine points came from three Tom Homer penalties.
Saracens won the match on the back of an immaculate kicking display from England fly-half Charlie Hodgson.
He landed five penalties from five attempts, struck two drop goals and converted Sarries' only try, scored by flanker Will Fraser.
But the victory was not enough to stop the reigning Premiership champions dropping from second to third as Leicester moved above them with their bonus-point win at Northampton earlier in the day.
Homer kicked Irish into the lead in the seventh minute with his opening penalty.
Saracens drew level three minutes later following a powerful rolling maul off the back of a lineout.
Referee Martin Fox allowed the visitors to play the advantage after the back-pedalling Exiles pack transgressed and Hodgson's superbly-executed drop goal ensured there was no need for the penalty kick.
Homer restored the home side's lead with a 15th-minute penalty after Saracens strayed offside.
He made it 9-3 with his third after 19 minutes when prop Matt Stevens, who was having a tough afternoon against England squad-mate Alex Corbisiero, was penalised at a scrum.
Hodgson reduced the deficit to three points with a penalty before out-of-favour England full-back Armitage, recalled to the Irish side as a winger, scored the opening try.
Centre Jonathan Joseph timed the final pass to perfection to send Armitage bursting through Sarries full-back Alex Goode's attempted tackle.
But Hodgson kept the visitors in touch with two well-struck penalties in the final four minutes of the opening half.
He struck from 45 metres when Irish were caught offside in the 36th minute and two minutes later the fly-half eclipsed that after Irish were penalised at the breakdown.
Referee Fox issued stern words of warning about the consequences of any repeat offences before Hodgson's 55-metre kick cleared the bar with plenty to spare.
The referee finally lost patience with the repeated London Irish infringements at the breakdown and he delivered on his first-half promise when he dispatched flanker Jamie Gibson to the sin-bin in the 52nd minute.
Hodgson kicked the resulting penalty to put Saracens ahead for the first time.
Saracens capitalised on their one-man advantage, winning a lineout and producing a 20-metre rolling maul which ended with Fraser touching down and Hodgson converting to put them 22-14 ahead.
But Irish, restored to 15 players, hit back with Armitage's second try.
Taking a pass from lock Bryn Evans, he stepped inside Sarries' centre Chris Wyles before beating two more defenders on the way to the line.
Hodgson eased any Saracens nerves with his fourth penalty in the 81st minute but two minutes later the visitors were reduced to 14 men when Fraser was yellow-carded for tackling Homer in the air as the young full-back collected a high kick.
Irish conceded two penalties as they tried to press home their advantage but Hodgson denied them even the consolation of a losing bonus point with his second drop goal in the final minute.
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