However, the Serie A outfit - who will compete in the Champions League next season - could not find a winner in the second half as Chris Wilder's side held out for an impressive result.
Goalmouth action was sparse in the first quarter of the match, with the hosts coming closest to opening the scoring when Jack O'Connell put a header over the crossbar in the 17th minute.
However, the Blades would take the lead against their illustrious opponents shortly before the half-hour mark when McGoldrick - who only completed his move to the club this afternoon - broke the deadlock after good work from Enda Stevens and John Fleck down the left.
It could have got even better for the Championship outfit just four minutes later when Fleck almost turned from provider to scorer, sending a dipping volley inches past the post with Samir Handanovic beaten.
Inter were level only three minutes after that, though, as captain Icardi - who has been linked with a mega-money move away from San Siro this summer - applied the finish touch to Andrea Candreva's cross 10 minutes before half time.
Icardi almost completed the turnaround with a second in quick succession moments later, but this time summer signing Dean Henderson was equal to the effort to keep the scores level going into half time.
That is how it would stay too, with clear chances at a premium during the second half, although United did almost steal a famous victory six minutes from time when Billy Sharp turned Andrea Ranocchia before getting a shot away which forced Handanovic into a smart save.
Mark Duffy also had a late sight of goal when he fired over as Wilder's side pushed on for the win, but they were unable to claim the significant scalp of Inter and instead had to make do with a draw against the three-time champions of Europe.
United now have just one pre-season match remaining - against Doncaster Rovers - before the start of the Championship campaign, whereas Inter will continue their European tour with International Champions Cup games against Chelsea, Lyon and Atletico Madrid.
SHEFFIELD UNITED: Henderson (Moore 46'); Baldock (Freeman 79'), Egan (Stearman 71'), O'Connell, Basham, Stevans; Lundstram (Duffy 61'), Fleck, Evans; McGoldrick (Holmes 71'), Clarke (Sharp 79')
INTER MILAN: Handanovic; D'Ambrosio, De Vrij (Ranocchia 69'), Skriniar, Dalbert (Roric 11'); Gagliardini, Asamoah, Martinez (Colidio 78'), Emmers (Pompetti 88'), Candreva (Zappa 64'); Icardi (Gavioli 78') body check tags ::