Syers, 24, who arrived at the Keepmoat from Bradford in June, volleyed in the equaliser after Martin Woods' early opener was cancelled out by a Rob Jones own goal and Craig Davies.
Scottish midfielder Woods fired a deflected strike past Tykes goalkeeper Ben Alnwick in the 13th minute before Rovers new-boy Jones turned Stephen Foster's cross into his own net.
Rovers goalkeeper Gary Woods saved from Matty Done early in the second half before Davies latched on to Jim O'Brien's pass to slot home from 15 yards with 19 minutes remaining.
But the lead did not last for long as Syers was on hand to find the empty net six minutes later.
