[1] Critical reception towards "Triumph of a Heart" was mixed; whilst some music journalists noted that it was one of the only radio-friendly songs on Medúlla as well as a successful album closer, others called the track "erratic".

The music video for "Triumph of a Heart", directed by Spike Jonze, depicts Björk being married to a housecat, going out for a night out on the town.

[5] According to Michael Hubbard from MusicOMH, the song begins with "balloons being blown up" and goes on to feature a sequenced cacophany of "meaows, mmmmms, parps, waaayaas and other side-splitting human voice noises all strung together like so many deranged pixies letting out their tensions in pixie disco land".

[6] "Triumph of a Heart" also features orchestral arrangements by the Icelandic and London Choirs,[7] as well as hooks coming from a "human trombone", the singer Gregory Purnhagen, and beatboxers Rahzel and Dokaka.

[1][8] Sal Cinquemani from Slant Magazine said the track "could be described as "future disco", with human voices subbing for bass kick, horns, house snare, and oscillating synthesizers".

[10] Dominique Leone, writing for Pitchfork magazine, said the track was one of the only songs on the album that might conceivably work on the radio.

[11] Chris Willman from Entertainment Weekly said "Triumph of a Heart" was "peppy" and "most easily digestible" than the rest of the album and "tucked away at the disc's end" it was like a "reward for making it through the more challenging passages".

[5] Justin Petrone of The Baltic Times newspaper said "Triumph of a Heart" was "as bouncy and pop as any of her best, a true symbol that the record has succeeded".

website commented that "she envelops all sensory perceptions on the breathy, beat-box laden" songs like "Triumph of a Heart".

[17] The Milk Factory website noted on the song there were hints of Björk's poppier days "cleverly blended into Medúlla's unconventional template".

[19] Matthew Gasteiser from Prefix magazine commented that "Triumph of a Heart" closes the album with an "awe-inspiring performance" by Dokaka, who "helps create a dance beat complete with trumpet that could have fit right in on 1993's Debut", and that along with "Who Is It", it was an "excellent addition" to her catalogue, but noted that "both seem to be bereft of instruments simply to serve the concept.

[20] Dom Sinacola from Coke Machine Glow website said that the track reunites "a clean menagerie of guest stars, rolling out Dokaka, Rahzel, and a bit of Schlomo for a tweaked disco boogie.

Whilst the "human trombone" of Gregory Purnhagen "intertwines itself with the dueling beatbox verbal acrobatics of Rahzel and Dokaka", it creates a "strange cross culture of head nodding dance music and fairy tale pop cacophony".

[34] "Triumph of a Heart" was first performed live on 20 April 2008 during the Volta tour at the Hammersmith Apollo in London.