Preheat oven to 400°F. Whisk chili powder, paprika, cumin, salt, and pepper in small bowl to blend. Rub spice mixture all over ribs. Place ribs in heavy large roasting pan.
Boil beer in medium saucepan until reduced to 1 cup, about 5 minutes. Pour beer around ribs. Cover pan tightly with foil. Bake ribs until fork-tender, about 1 hour 30 minutes.
Combine barbecue sauce, 1/2 cup water, brown sugar, and espresso powder in heavy medium saucepan. Simmer until flavors blend and sauce thickens slightly, stirring occasionally, about 10 minutes. DO AHEAD Ribs and barbecue sauce can be prepared 1 day ahead. Cool slightly, then cover separately and refrigerate.
Prepare barbecue (medium heat). Brush ribs with some barbecue sauce. Grill ribs just until heated through, about 3 minutes per side. Transfer ribs to platter. Bring remaining sauce to simmer. Brush ribs with more barbecue sauce. Serve ribs, passing remaining barbecue sauce separately.