Villa had taken an early lead in controversial fashion when Tammy Abraham's first goal since rejoining the club went unflagged for offside, with VAR not in operation in the competition.
Frustration grew for the Magpies when Lucas Digne appeared to handle the ball inside the area, yet referee Chris Kavanagh awarded only a free-kick outside the box. Even a late challenge by Digne on Jacob Murphy, which left the Newcastle forward with cuts, went unpunished beyond a yellow card.
The turning point came just before half-time when Villa goalkeeper Marco Bizot charged off his line to deny Murphy a clear goalscoring opportunity, leaving referee Kavanagh no choice but to issue a straight red card.
Newcastle capitalized on the numerical advantage, with Tonali equalizing from a free-kick that deflected past Emiliano Martinez. The Italian midfielder, who had not scored since May, doubled his tally with a stunning long-range strike to give the Magpies the lead. Nick Woltemade then sealed the win on his 24th birthday, ending a 14-match goal drought and sending 6,500 travelling Newcastle fans into ecstasy.
The victory ensures Newcastle advance to the last 16, with the next-round draw set for Monday, while Villa's hopes of ending a 30-year silverware drought now hinge on their Europa League campaign.
Tonali's performance, meanwhile, only reinforces why the Italian midfielder has been linked with a potential move to Arsenal at the season's end.
Newcastle captain Bruno Guimaraes faces a lengthy spell on the sidelines after suffering a hamstring injury in the closing stages of the Magpies' 2-1 Premier League win over Tottenham Hotspur on Tuesday.
Arsenal captain Martin Odegaard wants his team to do better in the FA Cup this season ahead of the fourth-round tie against Wigan Athletic at Emirates Stadium on Sunday.
Manchester City boss Pep Guardiola was happy to progress to the next round of the FA Cup after beating Salford City 2-0 but admitted his team's performance was 'flat'.
Liverpool advanced to the next round of the FA Cup after defeating Brighton and Hove Albion 3-0 in their fourth-round clash at Anfield on Saturday evening.
