Dumoulin (Giant-Alpecin) made a late surge along a punchy cobbled finale to double his overall lead over Fabio Aru (Astana) to six seconds. Joaquim Rodriguez (Katusha) is third at 1min 24sec.
However, Aru may have bigger troubles after apparently accepting a handsling from teammate Luis Leon Sanchez on a cobbled climb at 1.5km to go, as Dumoulin pulled away from the Astana rider, which could see him net a time penalty or even be ejected from the race like his erstwhile teammate Vincenzo Nibali.
The race jury has not yet decided whether Aru will be punished after reviewing the footage post-stage, but will review it and additional video evidence before the start of Stage 20.
The stage winner came from the breakaway of the day. A WorldTour professional for one season, the 22-year-old Gougeard finished ahead of veteran performers Nelson Oliveira (Lampre-Merida) and Maxime Monfort (Lotto Soudal) to collect the biggest win of his young career.
How it happened
The 185.8km stage from Medina del Campo to Avila Another was marked as a breakaway stage, and that's exactly as it played out with 18 teams represented in the break of the day.
The break had established a time gap of 15min 45sec to the peloton after 80km of racing. Its lead was enhanced by a crash in the main peloton, which slowed the chase. It also notably involved Aru, who picked himself up and quickly rejoined the peloton.
The stage opened up with 40km to go, when a series of attacks in the break ended in Gougeard dropping Tiago Machado (Katusha) with 22km left to race.
As Gougeard drove to the finish, the general classification favourites were engaged in a battle of their own, with Alejandro Valverde (Movistar) making repeated attacks off the from of the bunch, apparently attempting to crack Dumoulin.
However, the tables were turned with just 2km to race as Giant-Alpecin engineered a platform for their race leader to launch a counterattack.
The finish for the favourites ended in with Aru and Domenico Pozzovivo (AG2R) crossing the finish line three seconds behind Dumoulin and Dani Moreno (Katusha). Valverde led the rest across the finish six seconds later.
"We were able to control the stage the whole day and in the finale we had still Lawson [Craddock] and John [Degenkolb] with me in our 20-rider group," Dumoulin said. "The guys were amazing today. I was feeling OK. Of course I was tired but I knew the other were tired, too. I just wanted to give it a try in the finale and took three seconds for the GC.
"I am satisfied, every additional second is good," he added. "Tomorrow will be a decisive stage and a very tough one too."