Paul Warwick kicked the home side's only points up until Matt Lacey's late bonus point-saving try. A poor lineout ultimately saw Connacht slip up in the race for the Heineken Cup play-off spot, as Cardiff - four points below the Irish province and now with a game in hand - remain in contention.
Returning hooker Bernard Jackman - back from Ireland squad duty - sparked an early showing from Connacht as he carried well. But it was the Welsh - 32-17 conquerors of Munster three weeks ago - who looked the more purposeful.
Gareth Bowen's early penalty shot slid wide but from a 26th-minute Salesi Finau breakaway, Phillips outsmarted the Irish rearguard to dive over from a quick tap penalty. Bowen clipped over the conversion, but was wayward when Phillips ended a dogged spell of Scarlets attacking with his second, spinning past opposite number Tom Tierney for his second on 32 minutes.
The Scarlets - without regular skipper Simon Easterby - went 15-0 in front nine minutes after the restart, as a clinical Bowen punished a ruck infringement from 28 metres. After a Matt Mostyn break, a subdued Warwick wasted no time in replying for the home side, as his right wing 30-metre penalty sailed over.
Bowen chalked up his 114th league point with another penalty, and although Warwick replied and Lacey burrowed over in injury time, a first away success since their 26-15 defeat of the Borders on the opening night of the season belonged to the Scarlets.