The striker struck in first-half stoppage-time at a rain-lashed Port Harcourt and again five minutes into the second half of the final Group B match, where only pride was at stake.
Udoh had not scored in four Champions League matches since claiming a hat-trick in a qualifying victory over Etoile Sahel of Tunisia last April.
The barren spell ended after 46 minutes of the first half on a puddle-littered pitch as he punished a mistake by Sundowns goalkeeper Wayne Sandilands.
Udoh dispossessed Sandilands when the slow-reacting shot-stopper failed to clear a back-pass, evaded him and tapped the ball into the net.
A harshly awarded penalty after 50 minutes allowed Udoh to score again, placing the ball in the corner as Sandilands dived the wrong way.
Udoh has scored nine goals in the Champions League this season, three more than Reda Hajhouj from Raja Casablanca of Morocco, who play Wednesday.
John Uche scored from a free-kick to put Enyimba ahead after 25 minutes and Percy Tau levelled nine minutes later with a looping header while facing away from the goal.
Group B was reduced to three clubs after matchday one when Entente Setif of Algeria were disqualified over a pitch invasion.