The match at Sheffield's Crucible Theatre resumed at 4-4, with four-time world champion Higgins - 51 on May 18th - taking the first frame of the day with a break of 72.
Murphy, looking to end a 21-year wait for his second world title, hit back with an 88 as he won two of the next three frames to draw level at 6-6.
But the Englishman's error in the next frame let Higgins back in for a contribution of 57.
The Scot's break of 86 gave him a two-frame advantage, but Murphy won a scrappy 15th frame and was back level after Higgins missed a tricky red with the rest down the left cushion.
Their best-of-33-frames clash resumes at 20:00 CET Friday, with another eight frames to be played in the third of four sessions.
In the other semi-final, China's Wu Yize is 6-2 ahead against Northern Ireland's Mark Allen heading into Friday's second session.