Nick Evans added a second penalty but Quins did not score in the second half.
Brown then missed a penalty chance before a limping Nick Evans sent a last-minute drop-goal attempt wide.
Peter Hewat and Nick Evans exchanged two early penalties each, before Alfredo Lalanne's kick put Irish ahead.
McAlister returned but New Zealand then lost fly-half Dan Carter, who limped off to be replaced by Nick Evans.
To their credit, Quins responded superbly to the adversity, their makeshift scrum competing well and Nick Evans directing matters at fly-half.
But Sam Smith's try, which was improved by stand-off Nick Evans, brought 100 per cent Quins back to within a score.
Both Cipriani and Harlequins kicker Nick Evans wasted too many opportunities to put points on the board, to the frustration of their respective team-mates.
Fly-half Nick Evans departed injured in the 47th minute, before his replacement at number 10 Chris Malone was also helped off hurt later in the second half.
Tom Williams faked injury to allow fly-half Nick Evans to return to the field in a cup tie and director or rugby Dean Richards has since stood down.
Olly Barkley touched down and converted as the home side led 10-6 at the break - the centre also notching a penalty with Nick Evans kicking Quins' points.
Tries by Gonzalo Camacho and Tom Guest, along with a penalty try, aided by Nick Evans' 20-point haul with the boot, earned Quins' first win of the season.
The now notorious incident occurred during the Heineken Cup tie against Leinster in April when wing Tom Williams faked injury to allow fly-half Nick Evans to return to the field.
With quality kickers such as Sale's Charlie Hodgson, London Irish's Ryan Lamb and Harlequins' Nick Evans around, Bates says even seemingly harmless penalties can become a simple three points for some sides.
The Barbarians squad for the upcoming fixture includes Nick Evans and Joe Rokocoko of New Zealand, Dimitri Yachvili and Imanol Harinordoquy of France, James Hook, Duncan Jones and Dwayne Peel of Wales, Sergio Parisse and Mario Castrogiovanni of Italy, Francois Louw of South Africa, and Kahn Fotuali'i of Samoa.
Barkley missed another penalty with four minutes of the half remaining but, after Bath skipper Michael Claassens was shown a yellow card for a high and early tackle on David Strettle, Quins fly-half Nick Evans made no mistake with two penalties to give his side hope at the interval.
Ched Evans and Nick Montgomery then spurned chances to add to the lead as the visitors dominated possession.
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