The Sixers will get Golden State's 2015 second-round pick as part of the deal.
The key to the trade is fourth-year pro Turner, Philadelphia's leading scorer at 17.4 points per game. A restricted pending free agent, Turner has also provided 6.0 rebounds and 3.7 assists per game.
Allen has averaged 5.2 points and 4.9 rebounds in171 career games with the Sixers.
"We felt we needed to make this trade to strengthen the core unit and our bench," Pacers President of Basketball Operations Larry Bird said. "In Evan and Lavoy, we think we got two really good players that can help us and we look forward to what they can bring."
Going to Philadelphia is the 30-year-old Granger, who averaged 17.6 points per game in 2009 when he was named to an all-star berth.