The album received mixed reviews from music critics, some praising her softer tones and production, while some criticized the album's overproduction along with its lyrical content and the inclusion of spiritual aspects. The first single released from the album was "Guardian".
In June 2011, Guy Sigsworth, producer of Morissette's Flavors of Entanglement, wrote on Twitter that he was in Los Angeles working with a "certain amazing Canadian lady". On February 28, Morissette shared a video (shot in May 2011) of her recording a song, and Sigsworth's voice behind the scenes made it obvious she was working with him. In May 2011, Morissette shared a song called "Into a King", on the occasion of the one-year anniversary of her marriage, which was co-written with Sigsworth. She also recorded "Magical Child" for the compilation album Every Mother Counts. In November 2011, Morissette appeared on the American Music Awards, saying she had written 31 songs and had to choose the final twelve for the record.
Rolling Stone magazine announced that Morissette's new album would be released in June 2012 and shared the titles of songs "Havoc" and "Celebrity". The magazine also wrote that nearly every tune has a monster chorus. On May 2, Billboard magazine wrote that Morissette's new album would be released on August 28, 2012 through Collective Sounds. The album was distributed by Sony's RED in the States. On May 23, the album became available for pre-order at Amazon.com.
Havoc and Bright Lights received mixed reviews from music critics. At Metacritic, which assigns a normalized rating out of 100 to reviews from mainstream critics, the album received an average score of 55, based on 17 reviews, which indicates "mixed or average reviews". Many critics first complimented the album's more mature and warmer sound. Holly Gleason from Paste gave it a positive review. She stated "Twenty years later, the lithe songwriter embraces the same hybrid notion of introspection and sonics that are anything but singer/songwriterly. [Havoc and Bright Lights] embodies relief, release and refuge [...] Without being florid or cosmic, she beckons to a far more graceful, honest world." Sarah Rodman from The Boston Globe praised the album's "crisp, tuneful, warm, and sincere" tone, as well as the production of the album. However, she was critical on the album's songwriting stating that songs "Celebrity" and "Win and Win" were "clunkers". Nick Levine from BBC Music was equally positive saying the album brought out a more "mellow [Alanis] Morissette". However, he was critical on the production saying it was "too slick". Stephen Thomas Erlewine from Allmusic said the album "is as soothing as a Sunday afternoon nap or a warm bath: it's music for when you know you're right where you want to be." At American Songwriter, Eric Allen called the album an "intelligent and inspiring" work that has "winning results".The A.V. Club's Annie Zaleski found "Havoc And Bright Lights remains fearless and vibrant despite its shortcomings." Elysa Gardner of USA Today said that Morissette finally has "found her bliss."
However, the album did receive more scathing outcomes, mainly due to her musical style and her lyrical content, which was about spirituality and motherhood. Jonathan Keefe from Slant Magazine did state that Morissette's changes in music was her "best material", but said "Unfortunately, too many of the songs on Havoc lack that specificity and Morissette's inimitable POV [...] she spends most of the album sounding like she's leading a meditation." Hermione Hoby from The Observer was critical towards the album. She stated "[Alanis Morissette] appears to be very happy and very into motherhood. Which is great for her, but less great for her music." She then said "For the most part these songs are entirely lacking in bite, dragging through limp soft rock and even softer sentiments." Johan Wippsson of Melodic.net felt that Havoc and Bright Lights is "totally over-produced and completely lacks of any kind of soul." Joseph Viney from Sputnikmusic was negative towards the album, criticizing her lyrical content especially the song "Celebrity", and felt that the production of the album was too "slick". He then stated "Not even some admittedly slick production can drag this out of the mire." Hayley Avron from NME gave it 2 out of 10, resembling a negative review. Speaking of track "Woman Down", she said "The only real achievement here is an ironic one, as [...] Alanis somehow manages to make a feminist statement sound like a total affront to womankind" and stated the rest of the album was "teenage poetry, trowelled onto a bed of sift-rock cliché." Simon Price from The Independent gave it a very scathing review, awarding it one star out of five. He criticized the album's softer music and change, saying "Morissette is the sort of woman who does yoga to ensure she can still gaze at her navel" while criticizing her lyrical content, production and her inclusion of a more spiritual and religious tone.
Havoc and Bright Lights entered the Billboard 200 chart at number 5 with 33,000 copies, as her first top 5 album in the US since 2004's So-Called Chaos and her sixth top 10 album in the US overall. The album also debuted at No.1 on Billboard's Rock Albums and Indie Albums charts. Internationally, the album peaked at No. 1 in Canada, Italy, Austria and Switzerland, and at No. 2 in the Netherlands and Germany, where the album was also certified gold for shipments in excess of 100,000 copies.
In February 2012, Morissette announced a summer European tour to promote Havoc and Bright Lights. Pre-sale started on February 8, while tickets went on sale on February 10. The first show took place Monday, June 25, 2012 in Birmingham. The first three tour dates, all in the United Kingdom, were sold out weeks before the tour started.