Felipe, who like Nikci was making his Bundesliga debut, gave Hanover a first-half lead before Klaas-Jan Huntelaar and Lewis Holtby scored in a 12-minute spell for the visitors.
Schalke, third last season, dominated the early exchanges and nearly took the lead when Holtby rounded goalkeeper Ron-Robert Zieler only to see his shot cleared off the line.
But Hanover took the lead completely against the run of play in the 43rd minute when Brazilian defender Felipe, who joined from Standard Liege in the close season, stooped to head in Christian Pander's free kick.
Dutchman Huntelaar, last season's Bundesliga top-scorer with 29 goals, equalised with a superb effort, unbalancing his marker with a couple of dummies before rifling his shot into the net, in the 52nd minute and Holtby gave the visitors a deserved lead in the 64th minute.
Zieler denied Schalke a third before Jan Schlaudraff burst into the Schalke area and laid the ball off for Swiss midfielder Nikci, who joined the team from FC Zurich, to equalise.