Tevez was an outcast under former Argentina coach Alejandro Sabella but was handed the chance to revive his career with the national team by new boss Gerardo Martino on Wednesday.
The South Americans ultimately had Lionel Messi and a deflected Cristian Ansaldi effort to thank for their win in east London.
Anas Sharbini had given the relatively inexperienced Croatia side a surprise lead 11 minutes in with a neat finish into the right-hand corner, and Argentina had to wait until the early part of the second half to restore parity.
Ansaldi's long-range strike took a wicked deflection off Sergio Aguero's hand to leave Lovre Kalinic helpless, before the Hajduk Split goalkeeper brought down Aguero inside the area - allowing Messi to put Argentina in front from the spot.
Tevez then made his first Argentina appearance since 2011 with his introduction off the bench and was greeted with plenty of applause from the crowd at former club West Ham.
While he was unable to get on the scoresheet, Argentina held out for a hard-earned win while Croatia will now turn their focus to Sunday's crucial Euro 2016 qualifier against Italy.
Despite the apparent gulf in quality and experience between the sides, with Croatia clearly having one eye on the weekend's clash at San Siro, Niko Kovac's side began well, with Sharbini ensuring an early lead as he netted his first international goal.
Mateo Kovacic’s run helped occupy the attentions of Federico Fazio and Pablo Zabaleta before the Inter man switched the ball wide for Sharbini to slot home and open his Croatia account.
Debutant goalkeeper Kalinic was tested by long-range strikes from Aguero and Angel Di Maria as Argentina continued to up the pressure in search of an equaliser after the half-hour mark.
Captain Messi found the side netting after a neat lay-off from Ansaldi inside the area and then saw a free-kick saved by Kalinic as a resolute Croatia stood firm to lead at the interval.
Barcelona's 18-year-old prodigy Alen Halilovic replaced Kovacic at the break but Croatia were quickly pegged back courtesy of Ansaldi's deflected strike.
The Atletico Madrid full-back controlled the ball smartly and let fly from distance to find the top corner, courtesy of a hefty deflection that appeared to strike Aguero on the hand.
Halilovic's attempts to restore Croatia's lead were thwarted as he was outmuscled by club-mate Javier Mascherano following a strong burst forward.
But it was another Barca man who put Argentina ahead when Messi stroked home a penalty three minutes short of the hour after Kalinic had felled Aguero inside the area.
The Argentina captain's first international goal came against Croatia in 2006 and, while the playmaker failed to add to his tally at Upton Park, Tevez almost sealed a goalscoring return with a header from Ever Banega's cross before seeing a strike pushed wide by Kalinic.
