THE Boss blasted David Letterman’s ratings through the roof this week.

Bruce Springsteen’s appearance on Thursday’s “Late Show with David Letterman” handed the show its best Thursday-night ratings since last December – when Rudy Giuliani put in his last “Late Show” appearance as the mayor of New York.

Thursday’s “Late Show” notched 321,000 households on Ch. 2 – 57 percent higher than the show’s usual Thursday-night edition.

NBC’s “Tonight Show,” hosted by Jay Leno, averaged 204,000 households on Ch. 4.

Overall, Thursday night’s Springsteen-juiced “Late Show” was seen in roughly 52 percent more area homes than the show’s weekly average.

Nationally, “The Late Show” averaged an overnight, metered-market rating of 4.0 – its best performance on a Thursday night since last May’s sweeps period.

Final national ratings for the late-night timeslot will be released by Nielsen later this month.

Springsteen – whose E Street Band includes “Late Night with Conan O’Brien” drummer Max Weinberg – also performed on last night’s “Late Show” and was expected to score another huge audience.

Springsteen’s appearances on “The Late Show” capped a week-long media blitz to promote “The Rising,” his first new studio album with the E Street Band since 1984.