Messi – who eclipsed Brazil great Pele as the all-time leading scorer for a South American nation during the previous international break – scored his 80th goal in an Argentina jersey on Monday (AEDT).
Argentina's all-time leading goalscorer saw his attempted outside-of-the-boot pass find the back of the net in the 38th minute before Rodrigo de Paul doubled the lead six minutes later, while Lautaro Martinez sealed the victory in the 62nd minute.
Lionel Scaloni's Argentina remain unbeaten through 10 qualifiers on the road to Qatar 2022 – six points behind leaders Brazil as they extended their undefeated run to 24 games across all competitions.
Uruguay entered the match without a win against Argentina since 2013, while La Albiceleste had never lost a home World Cup qualifier to La Celeste amid a run of five consecutive victories.
But Uruguay made a bright start in Buenos Aires, where talisman Luis Suarez was in the thick of the action.
Suarez and Uruguay were unfortunate to not score at least twice in the first half, with Argentina goalkeeper Emiliano Martinez proving an unbeatable object.
Martinez thwarted Suarez twice with two big saves, while the latter saw his acrobatic volley cannon off the post on the half-hour mark.
Argentina went close to breaking the deadlock in the 33rd minute following a swift counter-attack, however, Giovani Lo Celso's effort struck the crossbar.
The opener did come via Messi, albeit in fortuitous circumstances, after his attempted pass ended up in the back of the net seven minutes prior to half-time.
Argentina took a 2-0 lead into the interval when De Paul tucked away a rebound a minute before the break.
Uruguay introduced Edinson Cavani and Darwin Nunez at half-time in attempt to spark a comeback but Argentina could not be stopped as space opened up.
Lautaro Martinez – back in the starting line-up – made it 3-0 just past the hour after finding himself unmarked at the back post following De Paul's low ball across the six-yard box.
Argentina almost had a fourth with 22 minutes remaining, however, Fernando Muslera got down well to save Joaquin Correa's close-range shot and the Uruguay goalkeeper was on hand again to thwart Angel Di Maria six minutes later.