Leonardo Ramos' side took advantage of a slip-up from previous leaders Nacional – who lost 5-3 at Defensor Sporting on Thursday – with their home triumph over the struggling Fenix.
They made an ideal start, scoring inside the first minute thanks to striker Jonathan Alvez, but were pegged back on the stroke of half-time.
Hernan Novick was the scorer for the visitors, netting a 44th-minute penalty, setting up an interesting second half in Montevideo.
Danubio pressed for the goal with a series of attacking substitutions but they left it exceptionally late, with Alvez's second – which came in the fourth minute of stoppage time – proving the difference between the two sides.
River Plate also climbed above Nacional courtesy of a 3-2 home win over Juventud de las Piedras.
Twice River had given away leads, with Renzo Pozzi and Jonathan Blanes cancelling out goals from Martin Alaniz and Michael Santos for the hosts.
But Lucas Olaza struck the killer blow, with his 83rd-minute effort moving River into second.
Danubio, River and Nacional have all enjoyed spells at the top of the table this season, with the unpredictable nature of the season continuing on Thursday.
Nacional seemed set for victory thanks to Alvaro Recoba's fifth-minute strike but Defensor had other ideas, scoring five times in an incredible final 25 minutes.
Giorgian De Arrascaeta initially levelled proceedings in the 66th minute, before Ignacio Risso fired them ahead from the penalty spot.
Felipe Conceicao then made it three for Defensor, only for Ivan Alonso to score a penalty with three minutes to play for Nacional.
Felipe's fourth – quickly followed by another Risso penalty – did the job for the home side, but Gonzalo Ramos still found time to respond in a crazy end to the match.
At the other end of the table, rock-bottom Miramar Misiones fell to a 4-2 defeat against the Montevideo Wanderers on Saturday.
Other fixtures on Saturday saw giants Penarol concede twice in the last 15 minutes to lose 2-1 at Sud America, while Rentistas and Liverpool played out a goalless draw.
And also on Sunday, the league's top scorer Hector Acuna grabbed a double as Cerro won 3-2 at El Tanque Sisley, while Cerro Largo edged Racing CM 1-0 thanks to Fabricio Nunez's strike.
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