Post-apocalyptic drama “The Last Ship” bowed to pretty good numbers Sunday for TNT, even as the net’s “Falling Skies” opened its fourth season with its lowest premiere scores to date.

Nielsen estimates that “Last Ship” averaged a 1.2 rating/4 share in adults 18-49, a 1.4/4 in adults 25-54 and 5.3 million total viewers for its 9 p.m. premiere, making it the top cable premiere of the summer in the key demos. In total viewers, it outdrew the series premiere of ABC’s music competition series “Rising Star” and ranks first among all 2014 cable premieres.

The 1.2 rating in 18-49 is the second highest drama bow of the past month, ahead of the likes of Fox’s “Gang-Related,” NBC’s “Crossbones,” AMC’s “Halt and Catch Fire” and ABC Family’s “Chasing Life.” NBC’s “The Night Shift,” which benefited from airing behind “America’s Got Talent,” opened to a 1.6 rating in late May.

Two weeks ago, TNT opened “Murder in the First” to a 0.64 rating in 18-49 and nearly 3.8 million viewers for its initial airing.

“Last Ship,” based on a novel of the same name, tells the story of a lone unaffected U.S. Navy ship following a global pandemic that wipes out 80% of the world’s population. Eric Dane and Rhona Mitra star

Following “Last Ship” on Sunday, the 10 p.m. season premiere of “Falling Skies” did a 1.0 rating/3 share in adults 18-49, a 1.3/3 in 25-54 and about 3.7 million total viewers. Last year’s two-hour, third-season premiere did a 1.5 rating in adults 18-49 and 4.21 million total viewers.

Counting a quickie repeat that aired at 11 p.m., “The Last Ship” drew 7.4 million total viewers on Sunday. And including its midnight encore, “Falling Skies” attracted 4.7 million.