The Bulls left South Africa a fortnight ago with a strong squad for a two-match tour of Wales, knowing they needed strong results to maintain their chances of making the URC quarter-finals.
The move paid big dividends as they returned home with nine points after following up their big 47-7 win over Dragons a week ago with a victory over Scarlets this time out.
As a result, they have moved up to seventh in the URC standings with two games of the league phase remaining.
The Pretoria side got off to a flying start with Cheswill Jooste cutting through the Scarlets' defence after getting an inside pass from Harold Vorster to score the opening try in just the third minute.
The hosts answered back well with tries from Callum Woolley and Eddie James putting them into the lead.
Scarlets looked as if they were going to score a third unanswered try before a defensive turnover allowed Embrose Papier to turn defence into attack with a long run through midfield.
The ball then went through the hands as the Bulls looked to keep the play alive, with it eventually finding its way to Pollard in space, who finished off a lovely try.
Pollard hit both conversions, which put the visitors 14-10 up at half-time.
They had a difficult start to the second period though, with Stedman Gans and Francois Kloppers both receiving yellow cards, which reduced them to 13 men for a portion of the half.
The numerical advantage allowed Scarlets captain, Fletcher Anderson, to power over the line for their third try of the game, but Joe Hawkins missed the conversion again, so they led by just a single point.
The Bulls then turned to their forwards to win penalties and Pollard's boot to get them points as the Springbok pivot hit two long-range shots, which sandwiched a Hawkins penalty to put them 20-18 ahead.
With just six minutes left on the clock, Scarlets won a scrum penalty which was knocked over the poles by Hawkins to give the hosts a slender one-point lead.
The visitors thought they had won the game with a David Kriel try in the 76th minute but the TMO ruled the score out for a forward pass.
However, the Bulls were able to win a kickable penalty through a powerful driving maul in Scarlets half with seconds left on the clock.
Pollard stepped up and did what he does best to hand the Pretoria men a gritty but important 23-21 win.
Stormers head coach said his side stuck to the game plan and did the simple things right, which allowed them to claim a decisive 48-12 win over Glasgow Warriors in the United Rugby Championship.
Bulls head coach Johan Ackermann praised his side for a job well done in Wales but warned them their job in the United Rugby Championship is not complete.
The Lions extended their red-hot run in the United Rugby Championship with a commanding 33-21 victory over Connacht at Ellis Park.
The Stormers bounced back strongly in the United Rugby Championship by overpowering the Glasgow Warriors 48-12 in a top-of-the-table clash at DHL Stadium on Saturday.
