Dua Lipa and the ‘SNL’ writers didn’t let a certain gun-toting, dog-shooting politician off the hook … and instead made Gov. Kristi Noem the punchline to kick off the show.

The singer was the host and musical act Saturday night, and shouted out her new album “Radical Optimism” during her monologue. Dua explained the album title refers to “looking on the bright side of any situation.”

She proceeded to offer some examples with help from cast members in the audience, which is when Heidi Gardner stood up in a MAGA hat and said, “Hi, I’m South Dakota Governor Kristi Noem” … opening the door for Dua to cut her off quickly.

You gotta watch the punchline, but the point is there’s ZERO optimism about Noem at the moment … as she’s been lambasted for sharing the story of why she killed a puppy.

As we reported, Noem reveals in her memoir that she shot and killed the puppy because it was “untrainable” and “less than worthless as a hunting dog.”

Back to Dua … who, in addition to performing 2 new songs, dove into the Kendrick Lamar vs. Drake feud by playing a local news “culture critic” who breaks down the beef.

The joke was her character Wanda Weems knows squat about the “culture” and offers deep insight like … Kendrick describes Drake as Canadian because Drake is from Toronto.

It won’t go down as an ‘SNL’ classic, for sure, but the white anchors pretending to be Drake and Kendrick, and winding up to say the n-word … kinda saved the bit.

Let’s face it, it’s kinda hard for any spoof to top the entertainment of the real-life epic rap war, which saw 3 new songs drop — one from Drake and 2 from Kendrick — just this weekend.

On a positive note … Dua’s night on ‘SNL’ did include a guest appearance by Jerry Seinfeld. So, there’s that.