Fu saw Stevens recover from trailing 9-4 to 9-7 as the possibility of an unlikely comeback began to gather pace.
But the man from Happy Valley in Hong Kong held himself together well at the key moment as he produced a marvellous shot on the final pink to swing the white around the angles to land on the black.
After looking nervy for the previous three frames, he rammed the black into a middle bag to win the 17th frame and avenge a 10-3 loss to Stevens at the same stage of the tournament last year.
The former Grand Prix winner's reward is a meeting with Trump in the last 16 after the 2011 finalist completed a 10-5 win over Dominic Dale earlier in the day.
Fu benefited from a series of Stevens errors to move from 6-3 overnight to 9-4 ahead.
But Stevens rallied and was looking a picture of health when he ran in 65 and 53 in the 16th frame, but has ended up out in the first round a year after he reached the last four.
FIRST SESSION REPORT
Matthew Stevens produced a brave cut on a re-spotted black but it was not enough to stop Marco Fu opening up a 6-3 lead.
Stevens is a double World Championship finalist and lost last year's semi-final to winner Ronnie O'Sullivan, but the Welshman will need to unearth some of his better form if he is to overturn Fu's lead when they play to a finish on Wednesday afternoon.
Stevens could easily have trailed 6-1, but produced an immaculate cut on a re-spotted black to close to 5-2 behind before a knock of 74 helped him collect a second straight frame.
But Fu - from Happy Valley in Hong Kong - dominated the final frame of the session to regain a three-frame advantage as he looks to avenge a 10-3 loss to Stevens in the first round of last year's tournament.
Stevens won the fourth frame with an 83 after a 70 in frame three had helped Fu into a 3-0 lead. Breaks of 62 and 71 were good enough for Fu to move four frames clear before the shenanigans on the re-spotted black saw Stevens clamber back into contention.
In the final analysis, Fu will not be overly disheartened with the outcome of the session. He is looking for four more frames to secure a meeting with Judd Trump or Dominic Dale in the last 16.