The Giallorossi is under fresh management in the form of vaunted sporting director Monchi and new head coach Eusebio di Francesco as it seeks to improve on a second-place finish behind champion Juventus in Serie A last season.
It lost 2-1 to Monchi's former club Sevilla on Friday, though, and left Spain with a bitter taste in the mouth after a heavy loss at Balaidos.
The visitor found itself behind in the 16th minute when Federico Fazio gave the ball away at centre-back and then bundled over John Guidetti inside the area as he sought to recover, the centre-back giving away a blatant penalty that Iago Aspas stroked home, sending goalkeeper Lukasz Skorupski the wrong way.
Guidetti suffered an injury in the fall - later confirmed as a fractured right collarbone, which is expected to keep him sidelined for six weeks - and was replaced by Maxi Gomez, but the early change did not rob Celta of their momentum.
In the 23rd minute, the impressive Pione Sisto left two Roma players for dead near the half-way line with a cool drag back. The Denmark international then advanced towards goal, watched as the defence backed off and duly unleashed a brilliant long-range strike into the top corner.
It was 3-0 four minutes later, Daniel Wass shifting possession out wide on the right to Aspas, who delivered the ball to the back post, where Sisto was on hand to tuck it home.
Roma fall apart at the back again with four minutes to go before half-time, Aspas playing a one-two with Wass and bursting into the box to tuck a careful finish into the far corner of the net.
Celta eased up in the second half and Kevin Strootman was able to pull a goal back for Roma, gathering possession inside the area and stabbing home after a slick move involving Radja Nainggolan's pass and an Edin Dzeko flicked assist.
But Monchi and Di Francesco may still have some cause for concern as they seek to orchestrate a convincing display in their team's Serie A opener away to Atalanta next Monday (AEST).
Celta's Liga campaign opens at home to Real Sociedad on Sunday.