Alonso has been struggling this season, failing to finish on the podium in all three races so far. But his strong performance in cool, slippery conditions was a welcome confidence boost for Ferrari.
The two-time F1 champion from Spain completed 13 laps and set a fastest lap of 1 minute, 38.67 seconds — 1.402 seconds faster than Nico Rosberg and 1.462 quicker than seven-time champion Michael Schumacher.
The wet conditions at the Istanbul Park track caused problems throughout, with new drivers Paul Di Resta and Pastor Maldonado struggling to keep control.
Vettel earlier went way out on a right turn and his car slid across the track and into the crash barrier on the other side of the slippery surface.
The German driver began about midway through the session on intermediate tires just as the rain was getting harder, and he was undone on Turn 8 — the longest in Formula One at 2,000 feet.
"There was some water on the exit," Vettel said on race radio. "There was nothing I could do."
Debris flew off the car and the wheels were skewed. The F1 champion waited for track officials to reach him, and his mangled car was towed away. Team members cleared some debris as Vettel went back to the paddock looking stern-faced.
The 23-year-old Vettel, F1's youngest ever champion, leads Lewis Hamilton in the overall standings by 21 points after winning two of the opening three races. Vettel was second behind Hamilton three weeks ago in China.
It also was a bad morning for Hamilton, the 2008 champion from Britain, whose clutch stuck as he prepared to join the session late. He failed to even post a time.
Jenson Button, Hamilton's McLaren teammate, managed only four laps and was nearly 22 seconds slower than Alonso.
Renault pair Nick Heidfeld and Vitaly Petrov were fourth and fifth fastest, respectively, but limited themselves to only nine and 10 laps each.
Swiss driver Sebastien Buemi completed the most laps, managing 22 in his Toro Rosso and finishing ninth quickest.