[7][8] Billboard associate editor Jason Lipshutz remarked that Clarkson has struck this pose many times, further describing the record as less of a fist-pumping anthem than "Stronger (What Doesn't Kill You)" (2012) or "Breakaway" (2004).

[7] "Invincible" also features strings arranged and conducted by Oliver Kraus, which music critics also construed that it ratcheted up the intensity of the chorus as well as Clarkson's vocals.

4Music commended the song as an "empowering belter",[12] while Nolan Feeney of Time praised the record, saying that of all the artists Sia has collaborated with, few are more suited to the spotlight-averse songwriter's brand of "victim to victory" anthems than Clarkson.

[13] In her review for HitFix, Courtney E. Smith described the song as having the looks to combine that Clarkson backbone everyone so loved from tracks like "Since U Been Gone" (2004) and the aural architecture of David Guetta and Sia's "Titanium" (2011).

[8] Reviewing for Entertainment Weekly, Taylor Weatherby complimented the track, writing that "Invincible" is more focused on reminding fans of the powerhouse vocalist Clarkson is, and that she that her "Stronger" spirit hasn't changed.

[15] Reviewing for Idolator, Bradley Stern doubled that remark, saying that the song is as one might expect a pairing between the quirky singer-songwriter and the masterclass belter to be — emotionally earnest and vocally explosive.

[17] Following its official single release, "Invincible" debuted at number 39 on the Billboard Adult Pop Songs chart for the week ending April 6, 2015.

[21] Clarkson spends most of the video dancing around a warehouse full of cube-shaped floating lamps, which eventually shatter to reveal women who were previously hiding inside.

[22] Clarkson debuted "Invincible" in a live performance on the 2015 Billboard Music Awards at the MGM Grand Garden Arena on May 17, 2015, a day before its street date.