It took a great feat of seamanship to arrive at Titanic's position. Firstly, Carpathia was three and a half hours away. Chief Engineer Johnston diverted all steam to the engines and squeezed every ounce of power from the boilers. The ship was rated at 14 knots, but according to Rostron she made 17 that night.
Secondly, Carpathia had to sail through the same ice-infested waters that claimed Titanic. As Captain Rostron raced his ship to the stricken liner, "every nerve strained watching for the ice." Everyone kept a sharp eye. The first iceberg was spotted at around 2:35 am by Second Officer James Bisset (who - like Captain Rostron - was a future Commodore of the Cunard Line). Rostron recounts that it "lay two points on the port bow and...was betrayed by [a] star beam." This star, fortunately, reflected off the berg's surface and guided Carpathia safely past.
"If only some such friendly star had glistened into the eyes of the lookout on the Titanic," writes Rostron. "Ah, well, it was not to be."
References: Arthur Rostron, Titanic Hero: The Autobiography of Captain Rostron of the Carpathia (Gloucestershire: Amberley Publishing, 2011), 36-40.