Inter on verge of lifting Libertadores
The Mexican side took the lead on the stroke of halftime in the first leg of the final at their Omnilife stadium with a header by Mexico international Adolfo Bautista.
But striker Giuliano and defender Bolivar replied to put the Brazilians on the verge of their second title. Inter won South America's premier club trophy in 2006.
Inter had been wary of Guadalajara's synthetic pitch but their man-of-the-match Andres D'Alessandro said: "We did well on a pitch that we said was no excuse for not playing our usual game.
"We went out to play as equals and luckily we got an away victory which is always important. But it's still 50-50. The Chivas (Guadalajara) play well as visitors so we've got to be very careful," he told Fox Sports.
The return leg is next Wednesday at Inter's Beira-Rio stadium in the southern Brazilian city of Porto Alegre.