Coming off a week in which “The Book of Mormon” racked up 14 Tony noms, producers of the nothing’s-sacred tuner have a lot of options to capitalize on all the critical love.

So you probably wouldn’t expect them to sked an extra matinee performance — and offer it free to proven fans of the show.

That’s the plan for July 1, when one extra performance, the ninth that week, will throw open doors to those whose names are drawn from the pool of people who tried (and, most likely, failed) to get tickets to “Book of Mormon” via the show’s daily lottery for lower-priced seats.

It’s the latest fan-friendly step for the tuner’s producers, who find themselves in the enviable but tricky position of sustaining the current B.O. momentum and seeding the field for future sales, all without alienating the legions of “South Park” fans who helped jumpstart the buzz in the first place.

“Mormon” creatives Trey Parker and Matt Stone, who teamed with composer-lyricist Robert Lopez on the tuner, have amassed a huge following thanks to their long-running Comedy Central skein. And according to “Mormon” producers Anne Garefino and Scott Rudin, wooing those “South Park” enthusiasts — 26 million and counting on Facebook — has always been a vital part of the “Mormon” strategy.

“Our ‘South Park’ fans are fiercely loyal,” says Garefino, also the exec producer of the TV series. “They weren’t thrilled we had to push the 15th season back to get ‘Mormon’ up.”

When the tuner was conceived, producers couldn’t be sure “South Park” fans would line up for it. “For a lot of our fans, this is going to be their first Broadway show,” Stone says.

Adds Rudin, “We knew they would be the most loyal audience, but also the most suspicious.”

Seducing those “South Park” zealots began early, with one of the musical’s first public showcases occurring as part of a private event that catered to the Aint It Cool News crowd. A group of fans also was selected to augment the aud at the production’s traditional friends-and-family dress rehearsal.

At the same time, producers could exploit the musical’s link to the high-profile “South Park” property as an instant indicator of the show’s content — particularly the cheerfully blasphemous vein of humor that’s not exactly common along the Main Stem.

” ‘South Park’ is a currency, and it’s a big brand,” Rudin says. ” ‘The Book of Mormon’ was a dicey title without ‘South Park’ in there too.”

Like many shows along the Rialto, “Mormon” hosts a regular lottery for a tightly limited number of lower-priced seats, in this case offered for $32 as opposed to the standard pricetag that tops out at $142 (not including premiums).

With “Mormon” converting more and more Broadwaygoers, the lottery has turned into a popular event. Sometimes more than 400 people show up for a single perf; most don’t get in.

“Seeing people out there waiting in line and then probably not making it in, that’s such a different thing for us,” says Parker. “We’re used to making something that anyone can get on the Internet or on their TV.”

Hence the free perf.

Beginning May 8, anyone who signs up for the lottery, win or lose, will be entered into the drawing for the July 1 matinee, one entry per attempt. There’ll also be a quick-response code that hopefuls can use to acquire an extra entry.

The thinking was: The more often someone shows up for the lottery, the better chance of winning those free tickets. “Genuinely, the biggest fans of the show will have the biggest chance of winning,” says Elizabeth Furze, managing partner at marketing agency AKA.

“Mormon” will pick winners of the sweepstakes soon after the June 12 Tony ceremony and notify them by email, with each winner receiving a pair of free, general-admission ducats after confirming attendance.

The last time a tuner gave a freebie to fans, producers of the 14 1/2-year-old revival “Chicago” doled out every ticket to the Feb. 8 matinee to fans who could get 10 Facebook friends to like the tuner. It proved popular enough that the dedicated app overloaded and had to be shut down.

“Mormon” initiative is a more costly affair for producers, not only because a ninth perf entails overtime wages for cast and crew, but also because the show’s at the height of its post-opening earning power.

But with the tuner rapidly gaining new Broadway fans, the “Mormon” team aims never to lose sight of the old ones.

“We didn’t want to be in a place where we, in success, exclude them from the show,” Rudin says.

Bob Verini in Los Angeles contributed to this report.