The winger grabbed a second-half winner just four minutes after Darren Bent equalised for the visitors to earn a 2-1 victory at The Hawthorns
In-form Matt Phillips had given Albion the lead but the Rams hit back to beat a side in a higher division in the Cup for the first time since knocking out Sheffield United in 1986
West Brom lost to Sky Bet Championship Reading last season and the Premier League side repeated the trick against Derby having failed to recover from going behind, with Craig Dawson coming closest to levelling after hitting the post
Derby now have just one defeat in their last 12 games but it could have been different after they nearly gifted the Baggies an early opener
Scott Carson presented Salomon Rondon the ball on the edge of the box but was spared by a brilliant sliding challenge from Richard Keogh, who hooked Rondon's shot off the line
Despite the gaffe, Derby had begun the brighter but failed to threaten until the 23rd minute when Boaz Myhill, one of four Albion changes, turned Abdoul Camara's deflected cross wide
The Rams were more energetic than Albion but lacked the quality in the final third despite some snappy build up and, as they dictated the play, the game drifted towards half time
But 10 minutes before the break the hosts broke the monotony after seizing on more poor Derby defending
The visitors may have escaped the first time but paid the price when James McClean blocked Keogh's clearance.
Phillips still had plenty to do as the ball fell for him 25 yards out but advanced and drove a low effort past Carson from the edge of the box for his fifth goal in 11 games.
It was harsh on Derby but the Rams were yet to create a serious opening despite matching their Premier League hosts in midfield
Albion went for the kill and nearly scored a quickfire second when James Morrison fired over and, after the break, Ga reth McAuley headed over and Rondon fired wide after robbing Jason Shackle
But County turned the game on its head inside four second-half minutes through Bent and Ince
First Bent, who had been quiet, was granted too much time on the edge of the area to lash past Myhill from 20 yards after 50 minutes before Ince won it
The winger's run from his own half was halted by Morrison 25 yards out and, with the free kick slightly to the right, Albion expected a cross
Instead, Ince caught Myhill cold and aimed for the near post and the goalkeeper did not move as the 24-year-old curled in his ninth goal of the season
Dawson's header hit the post as Albion tried to respond and Ince forced Myhill into a fine stop as the game reached the tempo it never hit during a tepid first half
Derby poured forward with more purpose and it was the Baggies' time to wonder where the chances would come from as they were restricted to efforts from distance
The influential Ince was pulling the strings and his excellent run eventually saw Myhill beat away Bent's classy snap-shot with 14 minutes left
Albion's late pressure failed to pay off but Derby relied on an excellent reflex save from Carson in injury time as he turned Rondon's header over.
Source : PA