Disenchanted with Sub Pop and with the Smart Studios sessions generating interest, Nirvana decided to look for a deal with a major record label. Following repeated recommendations by Sonic Youth's Kim Gordon, Nirvana signed to DGC Records in 1990. The band subsequently began recording its first major label album, Nevermind. They were offered a number of producers to choose from, but ultimately held out for Butch Vig. Rather than recording at Vig's Madison studio as they had in 1990, they shifted to Sound City Studios in Van Nuys, Los Angeles, California. For two months, the band worked through a variety of songs in their catalog. Some of the songs, including "In Bloom" and "Breed", had been in the band's repertoire for years, while others, including "On a Plain" and "Stay Away", lacked finished lyrics until mid-way through the recording process. After the recording sessions were completed, Vig and the band set out to mix the album. However, the recording sessions had run behind schedule and the resulting mixes were deemed unsatisfactory. Slayer mixer Andy Wallace was brought in to create the final mix. After the album's release members of Nirvana expressed dissatisfaction with the polished sound the mixer had given Nevermind.
Initially, DGC Records was hoping to sell 250,000 copies of Nevermind, which was the same level they had achieved with Sonic Youth's Goo. However, the album's first single "Smells Like Teen Spirit" quickly gained momentum, thanks in part to significant airplay of the song's music video on MTV. As they toured Europe during late 1991, the band found that the shows were dangerously oversold, that television crews were becoming a constant presence onstage, and that "Smells Like Teen Spirit" was almost omnipresent on radio and music television. By Christmas 1991, Nevermind was selling 400,000 copies a week in the US. On January 11, 1992, the album reached number one on the Billboard album charts, replacing Michael Jackson's album Dangerous. The album also topped the charts in numerous countries worldwide. The month Nevermind reached number one, Billboard proclaimed, "Nirvana is that rare band that has everything: critical acclaim, industry respect, pop radio appeal, and a rock-solid college/alternative base."
In February 1992, following the band's Pacific Rim tour, Cobain married Hole frontwoman Courtney Love in Hawaii. Love gave birth to a daughter, Frances Bean Cobain, the following August. Citing exhaustion, the band decided not to undertake another U.S. tour in support of Nevermind, instead opting to make only a handful of performances later that year. Just days after Frances Bean's birth, Nirvana performed one of its best-known concerts, headlining at the Reading Festival in England. Amid rumors about Cobain's health and the possibility the band might break up, Cobain entered the stage in a wheelchair as a practical joke, then proceeded to get up and join the rest of the band in tearing through an assortment of old and new material. Dave Grohl related in 2005 on the radio program Loveline that the band was genuinely concerned beforehand that the show would be a complete disaster, given all that had happened in the months leading up to the show. Instead, the performance ended up being one of the most memorable of their career.
Less than two weeks later, Nirvana performed at the MTV Video Music Awards. During the first rehearsal for the show, Cobain announced that they were going to play a new song during the broadcast, and the band rehearsed "Rape Me". MTV's executives were appalled by the song, and, according to show producer Amy Finnerty, the executives believed that the song was about them. They insisted that the band could not play "Rape Me", even threatening to throw Nirvana off the show and stop airing their videos entirely. After a series of intense discussions, MTV and Nirvana agreed that the band would play "Lithium", their latest single. When the band began their performance, Cobain strummed and sang the first few bars of "Rape Me", one last jab at MTV's executives, before breaking into "Lithium". Near the end of the song, frustrated that his amp had stopped functioning, Novoselic decided to toss his bass into the air for dramatic effect. He misjudged the landing, and the bass ended up bouncing off his forehead, causing him to stumble off the stage in a daze. As Cobain trashed their equipment, Grohl ran to the mic and began yelling "Hi, Axl!" repeatedly, referring to Guns N' Roses singer Axl Rose, with whom the band and Courtney had had a bizarre encounter before the show.
Nirvana released Incesticide, a collection of rarities and B-sides, in December 1992. Many of Nirvana's radio sessions and unreleased early recordings were starting to circulate via trading circles and illegal bootlegs, so the album served to circumvent the bootleggers. The album contained songs from previously released singles and EPs, including "Sliver" and "Dive", as well as material from the band's sessions for the BBC, including "Been a Son", "Aneurysm", and covers of songs by The Vaselines and Devo.