Poels (Sky) finished the hilly 18.4km stage from La Fouillouse to Saint-Etienne in 25min 33sec to beat Movistar's Marc Soler by 11sec with Julian Alaphilippe (Quick-Step Floors) a further five seconds back.
Poels is now second overall at 15sec behind Sanchez, who was part of Tuesday's successful breakaway. Alaphilippe is third at 26sec.
"I saw this morning at the recon that it was a good course for me especially the first part," Poels said. "It was a very good TT for me especially after the bad luck I had yesterday when I had to change my back wheel as Luis Leon Sanchez had gone.
"I don't know if 15 seconds is too much, I hope not. We will see in the next couple of days. We were two leaders at the start and it did not change much because Sergio (Henao) also rode a good TT.
"It's probably better to have more leaders tactically. Changing from eight to seven riders makes it more tricky tactically but it's going to be interesting."
The fifth stage runs 165km run from Salon-de-Provence to Sisteron.
More to come.