Dwayne Roloson made 20 saves in defeat.
After a scoreless opening period, Zubrus gave the Devils a 1-0 lead early in the second with a short-handed wrister.
Less than five minutes later, Elias deked Roloson and buried a close backhand for a power play tally and a 2-0 lead.
Later in the second, Clarkson struck on the power play for his seventh goal of the season, giving the Devils a 3-0 advantage.
But St Louis initiated a third-period rally, making it a 3-1 game with a wrister past Brodeur at the 8:24 mark.
Shannon went short-side to make it 3-2 midway through the period, but Carter scored off of a Roloson turnover with 2:03 remaining to halt the charge and seal the Devils' victory.
This was the first of four meetings between the teams this season...Elias is now just four goals away from tying John McLean's club record of 347...Clarkson has goals in three straight games.