Both Nigerians made their 11th league appearances of the season, with Adams playing the entire encounter.
Following a goalless first half, Toma Bašić broke the deadlock in the 53rd minute before Matías Moreno's own goal restored parity four minutes later.
However, Kike Pérez struck a spectacular winner in the 65th minute to secure three crucial points for Davide Nicola's side.
The victory provided much-needed relief for Venezia, who had lost their previous three matches without scoring.
Meanwhile, Udinese's struggles continued under newly appointed manager Paolo Zanetti, who suffered defeat against his former employers.
Despite the result, Venezia remain in the relegation zone with six points, while Udinese sit bottom of the standings with five points.