Goals from Filipe Morais, Lucas Akins and James Dunne handed Boro their sixth away league victory of the season.
The high-flying visitors stormed into the lead after three minutes when midfielder Morais turned home Greg Tansey's cross after a mistake by defender Byron Webster. However, Yeovil hit back five minutes later when striker Paddy Madden, who last week extended his loan from Carlisle until January, fired Sam Foley's cross past Steve Arnold.
The hosts, who had won four out of their last five League One matches, continued to threaten before the break with Madden twice denied before Keanu Marsh-Brown's shot was blocked.
The away side started the second half brightly and restored their advantage after 50 minutes when Akins notched his sixth goal of the season after clinically converting substitute Marcus Haber's low delivery.
Stevenage added a third after 65 minutes when Dunne's low drive was cruelly deflected past goalkeeper Marek Stech.