Squeeze thawed spinach in a clean kitchen towel until very dry. Chop artichokes finely, spread over paper towels and press firmly to remove surface moisture.
Beat cream cheese, Parmesan, lemon juice, zest, garlic powder and pepper together in a bowl. Fold in spinach and artichokes, breaking up dense spinach clumps.
Spread one-quarter of the filling evenly over each tortilla, leaving only a 1/2-inch bare strip along the far edge. Roll snugly toward that strip without crushing the filling out.
Wrap each roll tightly and refrigerate for at least 60 minutes until firm. Keep the rolls horizontal so the filling remains evenly distributed.
Trim just enough from each end to expose a full spiral, then cut each roll into eight equal rounds with a sharp knife, cleaning the blade between cuts. Yield 32 pinwheels, two per serving; refrigerate covered and use within 24 hours.