Henrikh Mkhitaryan scored after just nine minutes as United dominated the first half, but Dennis Praet equalised in the 63rd minute.
The Red Devils almost made a disastrous start to the match, when David De Gea gave away an indirect free-kick six yards out after scrambling to keep out a dreadful backpass from Daley Blind.
However, the tide quickly turned; after preventing Sampdoria from capitalising on their position, Antonio Valencia led a rapid counter-attack before Matteo Darmian crossed for Mkhitaryan to head home from close range.
Football writer Liam Canning hailed the Italian following his assist:
He continued to look threatening going forward, as he put in another promising performance. But Blind's struggles also continued, and he almost allowed Fabio Quagliarella in by keeping him onside.
The Red Devils were otherwise comfortably on top, though, and Mkhitaryan twice came close with further headers, with the first saved by Christian Puggioni and the second glanced wide.
Romelu Lukaku also saw an effort deflected narrowly wide after cutting in from the right, while Andreas Pereira fired an effort over the bar.
Meanwhile, new signing Nemanja Matic took part in the first 45 minutes, and football writers Tom McDermott and Rob Dawson were both impressed:
United looked to have doubled their lead in the 62nd minute, when Marouane Fellaini found Ander Herrera for the Spaniard to lash home, but it was correctly disallowed for offside.
Sampdoria—who had improved since the restart—pulled level immediately, when Praet fired home a low effort from the edge of the area.
Samuel Luckhurst of the Manchester Evening News believed Chris Smalling to be at fault:
Anthony Martial's introduction proved fruitful, and soon after coming close to setting up Herrera, he picked out Mata following a lovely dribble. The Spaniard made no mistake from the edge of the area.
A strong finish from the Red Devils saw them force an excellent double save from Andrea Tozzo, who first kept out Herrera's volley from a corner and then denied Marcus Rashford on the rebound.