Messi converted from the spot midway through the first half after Guillermo Maripan brought down Lautaro Martinez in the box. Chile striker Sanchez levelled in the 37th minute, finishing off a cut back from Gary Medel.
Before the match, a statue was unveiled outside the Unico Madres de Ciudades stadium in Santiago del Estero, to honour Diego Maradona, who died last November.
"It was a very special game because it was the first without Diego," Messi said. "We know what the national team meant for him. Even when he wasn't present at the stadium, he was always supporting us. We wanted to give him the victory and represent Argentina as he always did."
Chile keeper Claudio Bravo made a world class save to keep the scores level just before half-time, tipping a Messi free kick round the post.
The match in Santiago del Estero was Argentina's first competitive outing since November and both sides looked rusty.
Argentina pushed forward as the game went on but Chile's rearguard was solid, even without their talismanic holding midfielder Arturo Vidal, who missed out after contracting COVID-19.
Messi almost snatched all three points in the last five minutes but could not find a way past Bravo.
The draw means Argentina are unbeaten at home against Chile in 35 matches, and have gone 12 games without defeat since losing to Brazil in the 2019 Copa America semifinals.
"It's been a long time since we played together," Messi added. "We didn't have qualifiers for a while so it's not easy to get together without enough time to train and keep playing at the same level. But I think we were very good.
"It was a difficult game as always against Chile, happy with the result and performance even though we couldn't get the victory."
Chile are sixth, with five points from five games.
The top four teams qualify automatically for Qatar while the fifth-placed side goes into an intercontinental playoff.