Mix paprika, black pepper, salt, sugar, and chili powder in a small bowl. Reserve 1 tablespoon of the dry rub mixture in a separate bowl for the mop.
Spread the remaining dry rub all over the brisket, coating thoroughly. Cover with plastic wrap and refrigerate overnight.
Prepare the mop by combining beer, cider vinegar, water, canola oil, Worcestershire sauce, minced jalapeños, and the reserved 1 tablespoon of dry rub in a heavy medium saucepan. Stir over low heat for 5 minutes.
Pour 1/2 cup of the mop into a bowl, cover and refrigerate for later use in the sauce. Cover and refrigerate the remaining mop.
Preheat oven to 375°F.
Place brisket fat-side up in a Dutch oven or heavy baking pan large enough to accommodate the brisket.
Roast brisket for 3-4 hours, basting with mop every 20 minutes, until tender.
Transfer brisket to a platter and let stand 15 minutes.
Combine barbecue sauce, chili powder, and any accumulated juices from the brisket in a heavy saucepan. Bring to a boil and thin with reserved mop if needed.
Slice brisket thinly across the grain and serve with sauce on the side.