The loss leaves the Exiles rooted to the bottom of the table and only the unlikely event of Bedford winning this season's Greene King IPA Championship would keep them afloat.
Other Championship title hopefuls Bristol, Yorkshire Carnegie and Doncaster have all met minimum standards criteria to play in the Premiership next season but, with Bedford not applying to have their ground audited, there is a lifeline lingering for Irish.
In the first half the hosts had no answer to the pace and attacking flair of Harlequins, when they trailed 19-3, but they responded with huge spirit to take their opponents all the way to the wire.
The bonus point win for the Quins ensured that, if they beat Exeter at home next weekend, they will have a European Champions Cup berth for next season without having to rely on beating Montpellier in the final of the Challenge Cup.
Charlie Walker scored two tries for Quins with Ross Chisholm and Kyle Sinckler grabbing one each. Ben Botica added two conversions and kicked a penalty with Nick Evans also slotting over a penalty and a conversion.
Luke Narraway, Asaeli Tikoirotuma and David Paice scored tries for Irish, with Theo Brophy-Clews kicking two penalties and two conversions, but they fell behind after only 10 minutes.
A clever pass from Danny Care sent James Horwill through a gap in the home defence before Walker was left with an easy run-in for the opening try. Botica converted before Brophy-Clews put Irish on the scoreboard with a penalty.
After 20 minutes, Quins scored their second try thanks to the efforts of Chisholm. First the full-back beat three players on a 35-metre run to set up a platform in the opposition 22 and, when the ball was recycled, a clever chip ahead from Chisholm was collected by Walker to score his second.
Two minutes later, Quins were over again when Chisholm got himself on the scoresheet as he finished off a flowing three-quarter movement, which had begun in the Irish half.
However, the hosts provided a spirited response to score their opening try as Quins suffered two blows in quick succession. First Jack Clifford was sin-binned for dragging down a maul before George Lowe left the field for an assessment, which allowed Irish to capitalise as Narraway finished off a driving maul.
Lowe returned at the same time as Horwill departed with an injury before Tikoirotuma rewarded a sustained period of pressure with a second try for Irish. Brophy-Clews converted before Botica kicked a penalty to give Quins a 22-15 half-time lead.
Irish were back on level terms after 55 minutes when Brophy-Clews converted a try from Paice, who crashed over from a driving line-out and they deservedly took the lead for the first time with a Brophy-Clews penalty.
However, the last 10 minutes saw Irish cruelly denied as Evans kicked a penalty and converted a try from Sinckler after the prop brushed aside a tackle to run 25 metres to the line.
The defeat leaves the Exiles clinging to the hope of a Bedford triumph in the Championship play-offs, but the Blues were downed 45-16 in the first leg of their semi-final with Bristol on Sunday.