But Frank Lampard’s men could not get back to winning ways after their 3-1 loss at Arsenal on Boxing Day, to be left instead with just one victory in their last five league matches.
Villa, by contrast, extended their unbeaten run to five matches, to sit fifth in the table and hold off Chelsea in sixth.
Chelsea boss Lampard made six changes from the Boxing Day defeat at Arsenal but will have been frustrated not to receive the upswing in performance he had demanded.
Villa’s neat build-up play and compact work off the ball kept Chelsea pegged back regularly throughout a cagey opening half-hour.
But just when Villa were gearing up to be reasonably satisfied with their work, Chelsea finally strung together a move of purpose and incision.
The first true flowing attack from the Blues yielded the breakthrough, as Chilwell delivered the telling cross – and Giroud applied the deadly finish.
Villa snatched an equaliser shortly after the break to halt Chelsea’s momentum, though the legitimacy of the goal would be long debated.
El Ghazi tapped home at the far post but would arguably not have had the space to do so had Grealish been censured for his tackle on Christensen in the build-up.
Villa managed to see the rest of the game out, leaving Stamford Bridge with a 1-1 draw.
