Scolari, who was sacked following Brazil's humiliating defeats to Germany and the Netherlands at the World Cup last month, took charge of Gremio for the third time in his career after Enderson Moreira was relieved of his duties.
But his first match at the helm resulted in a defeat to lowly Vitoria at the Estadio Manoel Barradas on Saturday.
Argentinean striker Hernan Barcos gave Gremio an 11th-minute lead - his third goal in two games - but it all went downhill for Gremio from that point as Vitoria netted two second-half goals through Caio - on loan from rivals Internacional.
Caio levelled proceedings on the hour-mark before he completed back-to-back braces with the match-winning goal 13 minutes from time.
The result helped Vitoria climb out of the relegation zone to 15th position with 14 points from 13 matches.
Gremio are only five points clear of Vitoria, having won only one of their previous eight league games.
Defending champions Cruzeiro (29 points) remain top of the standings, despite their 1-1 draw at lowly Botafogo.
Leo was the unlikely hero for Cruzeiro, scoring a 60th-minute equaliser to cancel out Edilson's first-half opener and earn the visitors' a share of the spoils in Rio de Janeiro.
Cruzeiro's lead at the summit has been cut to four points after Fluminense and Internacional recorded respective wins.
Fluminense accounted for Goias 2-0 on Sunday, while Internacional edged Santos 1-0 in a fixture that saw both teams finish the match with 10 men.
Corinthians missed the chance to close the gap to three points following their goalless draw at Coritiba.
In results elsewhere, two own goals helped Atletico Mineiro to a 3-1 triumph over Atletico PR.
Flamengo remain rooted to the foot of the table after they were beaten 1-0 by Chapecoense.
Vanderlei Luxemburgo's men have managed just one win from their past 10 games to occupy bottom spot with 10 points.
Sao Paulo's winless streak extended to three games as they played out a 1-1 draw at home to Criciuma.
Palmeiras and second-bottom Bahia drew by the same scoreline.
Meanwhile, third-bottom Figueirense disposed of Sport Recife 3-0.
