The Mexican, starting up front in the absence of the injured Robin van Persie, netted just 40 seconds after the restart as the Red Devils bounced back from their derby defeat
The Mexico international struck early in the second half, while Luis Suarez, returning to action after a 10-match ban for biting Chelsea's Branislav Ivanovic last season, came closest to leveling the scores with a free kick that clipped the crossbar.
The Uruguayan was restored to a strong Reds starting lineup, while Kolo Toure continued to deputize at right back.
David Moyes, meanwhile, made a number of alterations, with the likes of Rio Ferdinand, Nemanja Vidic and Michael Carrick excluded, though Wayne Rooney was handed the captain's armband as he started in attack.
Despite United making wholesale changes, the home side undoubtedly started the match with greater fluency than its rival, with Nani's powerful left-footed drive forcing Martin Skrtel into a block within the opening five minutes.
Suarez was presented with two promising opportunities soon after, but opted to shoot when he should have passed for the first before doing the opposite with his next chance as the visitors failed to find the breakthrough.
The Liverpool forward came even closer soon after, but could not catch up with a slightly loose touch from Jose Enrique's long pass, allowing David de Gea to gratefully collect at his feet.
Both sides had lacked quality when it mattered in the first half, but it did not take long for the deadlock to be broken in the second period.
The hosts underlined their intent as they burst forward in the opening seconds of the half, winning a corner almost immediately as Mamadou Sakho failed to clear. And, after easily escaping the attentions of Enrique in the box, Chicharito side-footed home to put United ahead.
Liverpool was somewhat unfortunate to go behind, and rallied well to create a number of good chances soon after; Jordan Henderson side-footed wide from inside the box before Suarez dragged an effort the wrong side of the post.
Victor Moses then had the visitors' best opportunity of the match in the 70th minute, but failed to direct his diving header either side of De Gea and allowed the Spaniard to palm the ball away.
Then, after substitute Shinji Kagawa's rasping effort had clipped the bar following a quick break, Suarez matched the Japanese by doing the same with a free kick that deflected off the wall and onto the woodwork.
Liverpool's search for an equalizer left a number of spaces for United to exploit, and Rooney almost made the visitors pay as he brought two brilliant saves from Simon Mignolet, but neither side could find the extra goal as United held on to take its place in the next round.