Brazil was on top for much of the game and created the better chances, but without Neymar it lacked a leader in attack and failed to beat a Panama side that have lost to the likes of Ecuador and Honduras since exiting the 2018 FIFA World Cup pointless.
Wearing Brazil's number 10 jersey — usually reserved for the injured Neymar — for the first time, Paqueta opened his international account just past the half-hour mark, although Panama equalised in contentious fashion through captain Adolfo Machado, who appeared to be offside.
An entertaining second half saw both sides hit the crossbar, with Brazil doing so twice, but neither side found a winner as the team ranked No.76 in the world held on for a memorable result in Porto.
Unsurprisingly, Brazil, which by contrast sits third in the FIFA rankings, took control early on and crafted a good number of chances, first going close in the 18th minute when Roberto Firmino headed Alex Telles's cross just wide.
Arthur was the next to threaten, twice shooting agonisingly wide of the left-hand post with long-range efforts about a minute apart.
Paqueta found the mark, however, latching on to Casemiro's brilliant cross from deep and guiding a volley in off the hand of goalkeeper Luis Mejia.
But Panama hit back, Machado, who was slightly offside, controversially heading Eric Davis's free-kick delivery beyond the stranded Ederson.
Richarlison almost restored Brazil's lead just after the break, only for his excellent volley from Fagner's cross to hit the bar.
Panama followed suit in the 62nd minute, as Harold Cummings' header came back off the frame of the goal.
Casemiro was the next to be denied by the woodwork 19 minutes from time, and Richarlison put the awkward rebound over, consigning Brazil to a woeful result, which could have been even worse had substitute Jose Fajardo's last-gasp volley not only hit the side-netting.