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Chris Ashton crossed the line for the game's first try on 23 minutes, although the resulting conversion was missed, keeping the scoreline tight in the opening quarter of the contest.
It looked as though the game was as good as over when Ashton added his second try of the night, leaving Owen Farrell to kick over for the extras, but Ulster regained some hope moments later.
First, Paddy Jackson kicked between the sticks to pull his side back into the quarter-final tie, before adding another to bring the scoreline to 17-15 with seven minutes remaining.
Mark Anscombe's charges were unable to find any more points in the closing stages, however, and Sarries held out to book their place in the next round.