On-loan striker Smith headed home in the first period and Emmanuel-Thomas added a cheeky second from the penalty spot in the second half, with Ben Nugent replying late on for the Glovers.
Smith shot wide after rounding Yeovil goalkeeper Jed Steer before his opener and fired over an open goal from six yards when set up by Mark Little.
Keiran Agard had a 25th-minute penalty saved by Steer, diving to his right, after being fouled by Brendan Moloney.
However, Smith would not be denied again as he rose powerfully at the far post to head home Joe Bryan’s 31st-minute chip from the left.
And substitute Emmanuel-Thomas doubled the advantage with the cheekiest of side-footed spot-kicks on 64 minutes after Greg Cunningham was judged to have been brought down by Nathan Smith.
Yeovil replied out of the blue with three minutes to go when centre-back Nugent fired a superb shot past Frank Fielding from 30 yards, yet it was too little, too late.