The Derby defence struggled to deal with Ipswich’s clever movement and incisive attacking play – particularly down the left flank against the outstanding Jack Clarke.
Clarke, Anis Mehmeti and Ivan Azon all provided a regular threat, with the opening goal also coming from a corner kick on the left where Travis got his positioning all wrong to send a textbook downward header past Rams goalkeeper Josh Vickers.
Mehmeti had the best chance to double the lead before the break, racing on to a delightful ball from Clarke that Vickers did well to block as he came rushing out of his goal.
Clarke then almost forced the Rams – and Travis – into conceding a second own goal, the Town winger dancing down the left once again and sending in a teasing cross that could easily have deflected home.
Derby had a couple of promising moments, but Patrick Agyemang missed the ball at the near post when attempting a tricky back-heel flick, David Ozoh headed an effort off target, and Brewster shot well wide from a tricky angle.
But the hosts lacked creativity and their opportunities were half-chances, while the visitors continued to look much more likely to add to their lead on the resumption.
Jack Taylor shot wide, and a fiercely struck Wes Burns half-volley forced Vickers into an excellent save.
However, having been second best for most of the game, Bobby Clark’s clever turn and the subsequent rash challenge by Azor Matusiwa enabled Brewster to blast home from the penalty spot to level the scores with 22 minutes remaining.
Both sides went close on a couple of occasions in the closing stages, the ever-involved Travis – who was dismissed in stoppage time for a second yellow card after a foul on Darnell Furlong – and Matt Clarke shooting over for the hosts but Davis had the final say.