Ulster failed to make a helping wind count in the opening 40 minutes.
Early pressure from the Scarlets was rewarded with a Jones penalty on six minutes with Schifcofske dragging his opening attempt wide of the posts two minutes later.
The best passing move of the half ended with Daniel's converted try after 18 minutes, with the winger darting past Andrew Trimble before touching down in the corner.
Schifcofske registered his first score in the 21st minute before Ryan Caldwell replaced Carlo del Fava, who suffered a shoulder injury in the opening minutes.
Ulster new boy Schifcofske went on to reduce the half-time gap to just a point when he converted two out of four penalties as indiscipline crept into the Scarlets play.
The wind was in the Welshmen's favour on the restart and they increased their lead through a Jones penalty on 42 minutes.
Jones failed to convert another penalty but the visitors began to take a grip on affairs and the fly-half fired the ball between the posts in the 58th minute to make it 16-9.
Ulster needed to press forward but found themselves camped in their own 22.
The Irish team launched an attack in the dying seconds but a handling error ended any hope of getting anything more than a bonus point from the game.
Ulster coach Matt Williams: "We just missed too many tackles - it's the same disease we had last year.
"It was a very soft try and we missed more than 20 tackles in the first half when you can't miss more than 10 in a game.
"We played in an extremely unorganised fashion in the first half."
Ulster: Schifcofske, Trimble, Cave, Dewey, Nagusa, Wallace, Boss, J. Fitzpatrick, Best, Botha, Del Fava, O'Donoghue, McCullough, Dawson, Diack. Replacements: Court for Botha (66), Caldwell for Del Fava (23), Pollock for Dawson (66). Not Used: Brady, Willis, O'Connor, Cunningham.
Scarlets: Stoddart, Daniel, Higgitt, G. Evans, M. Jones, S. Jones, Martens, I. Thomas, Rees, Meeuws, Reed, Maling, Easterby, G. Thomas, Lyons. Replacements: Roberts for Martens (70), Manu for Meeuws (66), Cooper for Maling (66), D. Jones for G. Thomas (66). Not Used: Owen, C. Thomas, Brew.
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