Liverpool midfielder Mac Allister swept in a low finish three minutes after half-time to break the deadlock at the Estadio Monumental in Buenos Aires against a defensive Chile side.
Former Manchester City striker Alvarez doubled the lead in the 84th minute with a thumping shot from outside the area before substitute Dybala put the seal on the victory with a late strike in stoppage time.
It was another clinical victory for the reigning world champions, who are now cruising towards confirming their place at the 2026 finals being staged in the United States, Mexico and Canada.
Lionel Scaloni's team lead South America's 10-team round-robin qualifying table by five points after seven games.
The top six teams in the final standings qualify automatically for the 2026 finals in North America with the seventh-placed team advancing to a playoff.
Argentina, who also beat Chile 1-0 on their way to clinching back-to-back Copa America titles earlier this year, went into Thursday's game missing injured captain Lionel Messi and veteran winger Angel Di Maria, who retired from international football after the Copa America triumph in July.
Di Maria was feted by his former teammates at a pre-game ceremony before taking his place in the stands to watch the world champions secure their sixth win from seven qualifying games.
Despite the absence of Messi and Di Maria, Argentina had plenty of creative guile in attack with Lautaro Martinez and Atletico Madrid's Alvarez causing problems for the Chile defense.
Argentina, meanwhile, controlled midfield with Mac Allister lining up alongside Rodrigo De Paul and Enzo Fernandez.
After a cagey first-half, the breakthrough came in the 48th minute when Alvarez whipped in a low cross from the right.
Martinez dummied cleverly and allowed the ball to roll through to Mac Allister, who guided an accurate shot into the bottom corner.
Bolivia thrash Venezuela
In Thursday's other qualifier, Bolivia reignited their campaign with a 4-0 drubbing over Venezuela in a game played more than 4,000m (13,100 feet) above sea level.
Goals from Ramiro Vaca, Carmelo Algaranaz, Miguel Terceros and Enzo Monteiro handed Bolivia only their second win of qualifying and lifted them into seventh place in the standings.
The result was a vindication of Bolivia's move to play Thursday's game in El Alto -- Spanish for "The Heights" -- rather than at their usual home venue in neighboring La Paz, which is 3,600m above sea level.
The thin air of El Alto clearly left Venezuela's players struggling for energy against a Bolivian team aiming to qualify for their first World Cup since reaching the 1994 finals in the United States.
Despite his team's heavy loss, Venezuela coach Fernando Batista refused to dwell on the altitude issue after the game.
"Out of 10 questions, eight are about altitude," Batista said. "You won't hear anything from me about it."
The pick of Bolivia's goals came from Vaca after just 13 minutes.
The 25-year-old midfielder gathered the ball around 30 yards from goal, cut in from the left and unleashed a ferocious shot which flew into the top corner.
Venezuela, the only team from South America never to have qualified for a World Cup, remain well-placed to reach the finals despite Thursday's loss.
The 'Vinotinto' are fourth in the standings with nine points from seven games, trailing Argentina, Uruguay and Colombia.
Venezuela host Uruguay next Tuesday in their eighth game of qualifying.
South America's qualifiers continue on Friday with second-placed Uruguay hosting Paraguay in Montevideo while struggling Brazil, who are 11 points adrift of leaders Argentina in sixth, face Ecuador in Curitiba.
Third-placed Colombia, meanwhile, travel to Lima to face bottom-of-the-table Peru.
