Matt Lauer played DJ when he and wife Annette hosted an intimate engagement party for “Today” co-host Savannah Guthrie and fiancé Mike Feldman Thursday at Isola Trattoria at the Mondrian in Soho. “Matt made his own playlist,” said a spy, adding that Lauer plugged his iPad into the restaurant’s sound system to pump tunes ranging from Marvin Gaye and the Isley Brothers to Gotye and Foster the People. Spotted mingling and congratulating Guthrie and Feldman were Jon Bon Jovi, Seth Meyers and Alexi Ashe (also newly engaged), former Obama speechwriter Jon Lovett, Kristin Gore, Bill Thompson strategist Jonathan Prince, screenwriter Brian Koppelman, Bryant Gumbel, Brian Williams, Meredith Vieira, Willie Geist, Jenna Bush Hager and Ronan Farrow. Guests munched at stations serving up Kobe corn dogs, sliders, dumplings and salt-and-pepper shrimp. “There was a really warm feeling,” said a guest of the bash, which went on until the lights came up at 9 p.m., which, a spy said, is “usually past the bedtime” of most of the “Today” crowd. Sources tell us Guthrie and Glover Park Group head Feldman haven’t yet set a wedding date.