Bryce Salvador, Lee Stempniak and Jay McClement also scored for St. Louis, which won for the second time in its last eight games. Back-up goalie Curtis Sanford made 31 saves for the Blues.
Rookie Brad Winchester scored twice for the Oilers. Fernando Pisani had the other Edmonton goal.
St. Louis led 3-2 early in the third period when Stempniak gave the Blues some insurance. He took a pass from Keith Tkachuk, skated down the left wing and lifted a backhander over Edmonton goalie Jussi Markkanen.
Pisani cut the advantage in half with a power-play goal with 3:32 remaining, but Rucinsky put the game away with an empty net goal with four seconds remaining.
The Blues briefly had a two-goal advantage in the second period. Rucinsky gave the Blues a 2-1 lead when he beat Markkanen with a wrist shot from the left circle at the two-minute mark. McClement made it 3-1 when he swatted home the rebound of Eric Brewer's shot at 18:39 of the period.
But Winchester got the Oilers back in it before the period was over with his second goal. Winchester broke into the St. Louis zone and surprised Sanford, who was screened by Brewer, with a wrist shot from between the circles with 4.6 seconds left.
A similar event occurred in the first period when Salvador gave the Blues a 1-0 advantage on a slap shot from the left point at the 14:03 mark. Just 42 seconds later, Winchester tied the game 1-1 off a scramble for a loose puck in front of Sanford.
Notes: St. Louis begins a five-game road trip starting in Calgary on Tuesday night and will not return to the Scottrade Center until Nov. 25. ... Winchester has three goals in his last four games. ... Rucinsky's goal was his first since Oct. 17. ... Blues defenceman Matt Walker left the game with a groin strain and did not return.