St. Louis got on the board early on as Doug Weight wristed a shot from the right circle that eluded Oilers goaltender Jussi Markkanen on the blocker side.
Before the period was 10 minutes old, St. Louis scored again to double their lead. Peter Sejna's shot from the high slot was knocked away by the glove of Markkanen and as the Oilers goaltender tried to reposition himself in the net Sejna banked the puck off him from behind the net.
The Oilers had some trouble getting anything going, outshot 12-2 13 minutes into the period.
Jussi Markkanen made a pair of big saves late in the period, first stopping Jamal Mayars on a blast from the right circle and then denying Lee Stempniak on his rebound attempt.
The stops may have inspired the Oilers as they came out on the next shift and scored to cut the Blues' lead to 2-1. Hemsky took a pass across the neutral zone from Jason Smith and broke into the Blues end at full speed. He deked out Jason Bacashihua before putting the puck in.
Less than a minute later, the Oilers struck again. Tom Gilbert pinched in to draw the Blues goaltender towards him before dishing it to Mathieu Roy in the slot. Roy slapped it into the open cage to tie the game at 2-2.
After leading 12-2 in shots early on, St. Louis only ended up outshooting Edmonton 14-10 after 20 minutes.
Midway through the second, the Blues scored to regain the lead at 3-2. Lee Stempniak made a nice move to keep the puck in the zone before spinning into the slot and firing the puck over the shoulder of Markkanen.
St. Louis regained their two-goal lead later on in the period after Weight made a nice play on a two-on-one centering the puck to Jay McClement who blasted a one-timer to make it 4-2.
Hemsky just about got his second of the game with just over two minutes to play in the middle frame. Hemsky broke in behind the St. Louis defence and had Bacashihua beat but couldn't get a handle on the puck.
St. Louis outshot the Oilers 15-3 in the second and 29-13 overall through two periods.
With Edmonton on the power play early in the third, Joffrey Lupul came within inches of scoring as his backhand attempt went just wide of Jason Bacashihua.
Another close call several minutes later as the Blues looked to have scored but Tom Gilbert was able to pounce on the puck after it hit the post and keep it from sliding across the goal line.
St. Louis added an empty netter to seal the deal, winning 5-2.