Lando Norris finished second for McLaren, with Aston Martin's Fernando Alonso holding off Verstappen's Red Bull team-mate Sergio Perez by just 0.053 seconds for third.
But it was an abysmal afternoon for Mercedes, with Lewis Hamilton eighth and George Russell forced to retire his car with an engine failure 12 laps from the end. Hamilton crossed the line an eye-watering 63 seconds behind.
The race in Sao Paulo was suspended following a chaotic start which saw a loose tyre hit Ricciardo's rear wing following a collision between Alex Albon and Nico Hulkenberg.
Albon, 13th on the grid, drew alongside Hulkenberg ahead of the first corner, but the two machines made contact, sending the London-born driver into Hulkenberg's Haas team-mate Kevin Magnussen and then into the barrier.
The force of the impact tore the left-rear off Albon's Williams, with the bouncing tyre - which weighs 13 kilograms - narrowly flying over the top of Ricciardo's head before smashing into the back of his AlphaTauri.
Footage from Ricciardo's cockpit shows him turning sharply to the left to avoid the flying rubber.
"I tried to miss it, but the tyre was in the air and it clipped my rear wing," he said.
The Australian driver, 34, was able to limp back to the pits for the repairs following the fortunate escape, while both Albon and Magnussen emerged unscathed.
Hulkenberg was able to carry on before the race was red-flagged for 25 minutes as the tyre barrier on the approach to the opening bend was repaired following Albon's shunt.
Norris lined up in second place for the restart following a fine getaway by the British driver from sixth. Hamilton made up two places from fifth to take third on the grid for the second start.
Verstappen mastered the getaway to keep his Red Bull ahead of Norris before Alonso made light work of Hamilton to gazump the British driver at the Curva do Lago.
On lap eight, Norris was suddenly in Verstappen's slipstream and for a handful of corners it looked as though he could do the unthinkable and take the lead.
Norris drew alongside Verstappen at the outside of Turn 4 to provide the Dutchman with a rare fright. But by the start of the lap, Verstappen had established a lead of more than one second, and for Norris, Verstappen was out of DRS range.
Behind, and it was starting to unravel for Mercedes. Performances at the previous two rounds had afforded Hamilton and the grid's once-all-conquering team hope that they were closing the gap to the top. But they were dealt a desperate reality check here.
On laps 14 and 18, Perez cruised ahead of Russell and Hamilton respectively before Russell bemoaned that he was being held up by his team-mate.
"Are we working together, or are we just doing our own races?" Russell asked.
Hamilton stopped for rubber, with Russell following his team-mate in on the next lap. Perez came in three laps later than Hamilton and had to re-pass the seven-time world champion, which he did with ease on lap 23. Aston Martin's Lance Stroll then blasted his way past the out-of-sorts Mercedes pair.
Russell, now seventh, was growing increasingly frustrated with Hamilton struggling for pace. Russell wanted Mercedes to order Hamilton out of his way.
"Do you want me to race or concede positions?" he asked.
Later, he added: "I haven't been on the radio because I thought it was quite obvious about the pace."
Mercedes were unmoved as Russell tried and failed to make his way ahead of Hamilton.
Carlos Sainz was soon all over the back of the squabbling Mercedes men, cruising past Russell on lap 35, and then Hamilton two laps later.
The Silver Arrows tumbled back through the field, with Alpine's Pierre Gasly moving ahead of Russell for eighth on lap 43.
Russell stopped for a second time on lap 45 with Hamilton in a lap later, only for Gasly to take another position off Hamilton to leave the seven-time world champion in eighth - that is where he would finish.
Hamilton now trails Perez by 32 points in the race for runner-up after the Mexican failed to take the final spot on the podium.
Perez got ahead of Alonso on the penultimate lap only for the Spaniard to blast back ahead on the last lap. The two drivers then went toe to toe on the drag to the finish line, with Alonso narrowly remaining ahead.