Argentina topple Spain for winning United Cup start
The South Americans got over the line at RAC Arena in Perth after 66th-ranked tournament debutant Sierra held her nerve for a 6-4, 5-7, 6-0 defeat of Jessica Bouzas Maneiro.
World number 45 Baez got his country on the scoreboard with a 6-4, 6-4 beating of Jaume Munar, earning a surprise win on hardcourt after just three victories in nine matches on the surface last season.
Baez gained control at 4-4 by breaking Munar and serving out the set in the following game.
In the second set he showed composure again by breaking back immediately after losing serve for a 4-3 lead and never looked back.
"I really enjoyed this moment, enjoyed the time on court, so happy to have won this point for Argentina," he said.
Greece, spearheaded by Stefanos Tsitsipas and Maria Sakkari, play the night session at the 18-nation event, taking on a Japan team led by Naomi Osaka.
Ties comprise one men's and one women's singles and a mixed doubles, with group winners in each city advancing to the quarter-finals along with the best runner-up.
Sierra led Bouzas Maneiro by a set and 5-2, but the Spaniard regrouped, showing grit to claw back and take it to a third set.
"It was a really tough match, I had to focus on my game," Sierra said. "I'm proud that I kept going and won in the third set."
The 21-year-old, who reached the fourth round at Wimbledon last year, added: "I knew I had to be tough. I'm super-happy with my level."