Aspas enhanced his burgeoning reputation with a fine run and finish from Michael Krohn-Dehli's through ball after just eight minutes, but Valladolid were back level moments later when Alberto Bueno converted from the spot after Javi Varas had brought down Javi Guerra.
However, Aspas restored the lead with a penalty of his own on the half hour mark and Alex Lopez sealed the points seven minutes into the second-half with a brilliant strike from 25 yards that rocketed into the top corner.
The visitors were missing their three most important attacking players in Patrick Ebert, Oscar Gonzalez and Manucho, but it was their usually solid defence that was found wanting as Celta scored three times for the first time in a league game this season.
Aspas punished Valladolid's high-line at the first time of asking as a quickly spotted through-ball from Krohn-Dehli released him in behind the defence and he calmly took a touch before sweeping the ball past Dani Hernandez into the top right corner of the net.
All of Celta's early good work was undone three minutes later though as Varas made a horrible mess of a routine clearance to present Guerra with the ball inside the area and then compounded his initial error by bringing down the striker with a desperate lunge.
Indeed the goalkeeper could count himself lucky not to have been sent off for denying a clear goalscoring opportunity, but he could do little to stop Bueno levelling the scores as he fired straight down the middle of the goal.
The game continued to rage from end-to-end during an entertaining first-half but it was Celta who were gifted the opportunity to retake the lead as Mikel Balanziaga was adjudged to have pushed Aspas as he tried to connect with a cross from the left despite there appearing to be little contact.
Aspas' successful first effort was ruled out for encroachment by a Celta colleague but he composed himself to convert from the second time to register his eighth goal of the season.
Celta began brightly again after the restart as Mario Bermejo's crafty lob was just clawed to safety by Dani, but there was nothing the Valladolid keeper could do to prevent the hosts' extending their advantage moments later as Lopez unleashed an unstoppable effort into the top corner from 25 yards.
Varas then had to make a couple of good saves from Luis Sastre and debutant Daniel Larsson to prevent Celta enduring a nervy finish but they were more than deserving of the win that moves them up to 15th with Valladolid remaining in 11th.