Tony Dokoupil’s “CBS Evening News” eked out 4 million viewers for the first time in weeks – though the show remains firmly stuck in third place behind its broadcast rivals.

In the five-day period ended May 22, “CBS Evening News” raked in an audience of a little more than 4 million, according to Nielsen data. It also clinched 605,000 viewers in the coveted advertising demographic of people age 25 to 54.

Dokoupil’s nightly broadcast saw only 3.8 million viewers, 482,000 of them in the key advertising demo, the previous week.

It’s a sign that Dokoupil – whose time in the anchor chair got off to a rough start in January with an awkward on-air blunder – is finally starting to make some viewership gains.

But CBS News is still far behind its rivals. 

David Muir’s “ABC World News Tonight” led broadcast ratings with 8.2 million viewers and 966,000 in the 25-54 demo in the week ended May 22.

“NBC Nightly News,” anchored by Tom Llamas, notched 6.1 million total viewers, 867,000 of them in that demo.

“If barely scraping past 4 million viewers counts as success at CBS News these days, they may want to revisit the definition,” an industry insider told The Post on Wednesday.

Meanwhile, Dokoupil has been facing intense scrutiny since he stumbled through his first broadcast in January, tripping over a teleprompter change and leaving viewers with several seconds of dead air as he struggled to decide which segment to report.

His own colleagues bashed him as a “useful idiot” and “good eye candy” in a brutal Vanity Fair report published last month.

“Tony has the biggest case of imposter syndrome out of any anchor or correspondent I’ve ever worked with,” a former producer who worked with him told the mag, describing the anchor as out of his depth.

Insiders told Vanity Fair that Dokoupil was actually CBS News editor-in-chief Bari Weiss’ “seventh or eighth choice,” after initially pursuing bigger names like Bret Baier and Anderson Cooper.

But a source close to the network told The Post that senior CBS News execs have attributed the recent ratings gains to the work of Dokoupil and his team, including his feature segments.

CBS News has fallen below 4 million viewers on many weeknights, starting when it ran a version of its evening newscast with two anchors last year in a failed attempt to win over NBC News viewers while the rival transitioned from Lester Holt to Llamas.

But last week marks the fourth consecutive week of viewership growth for “CBS Evening News,” according to Nielsen. So far in May, the show has seen 4% more viewers than this time last year and 6% more in the key 24-54 demographic.

“ABC World News Tonight” remains the undisputed top nightly network news broadcast, according to Nielsen ratings. 

Its lead over CBS News’ evening show – by 4.3 million viewers – is its largest gain over the Tiffany Network in 34 years, since Nielsen started keeping records.

ABC also holds its largest lead over NBC in more than 30 years, with nearly 2 million more viewers.

“NBC Nightly News,” meanwhile, has notched its longest streak of viewership growth in the key advertising demo, closing in on ABC’s lead.

The network is also holding its largest total viewership lead over CBS in six years.