The visitors left south Yorkshire with all three points after a performance which saw them score with their first three shots on target.
Conor Hourihane and Matt Grimes produced two fine strikes inside 10 first-half minutes to help win a closely-fought contest against a Rotherham side who will not feel too down-hearted after a promising display.
The opener arrived as Yan Dhanda knocked the ball down for Hourihane who arrowed an effort into the bottom right-hand corner. United manager Paul Warne claimed the on-loan Aston Villa man had the "best left foot in the league" in his pre-match comments with the goal his second in as many games since signing for the Welsh club.
Another sweet left-footed strike doubled the advantage as Grimes fired the ball into the net after Jamal Blackman had punched clear.
Freddie Ladapo gave Rotherham hope with a second-half header but hopes of a fightback faded as Jay Fulton added a third for Swansea following a swift counter attack.
The Millers had come into the contest in a bullish mood after they recorded a 3-0 victory at Middlesbrough in midweek.
December was a month to forget for Warne's side as they lost five of their six matches in the final month of 2020, however, a new year brought new resolve for the Millers.
They pushed Premier League Everton all the way in the FA Cup third round, eventually losing 2-1 after extra time.
That performance helped restore belief as they went on to win 1-0 at Derby County and draw 3-3 at home to Stoke City before this week's win at the Riverside Stadium.
Games against the sides chasing promotion won't define Rotherham's season as attentions now turn to a crunch battle with Derby on Tuesday night.
Rotherham started Saturday afternoon's contest on the front foot, winning the ball back aggressively and asking questions of the visiting defence.
However, Swansea seemed to have all the answers as their rise up the Championship table can be attributed to their strength at the back.
Steve Cooper's side had conceded just 14 goals in 25 league games prior to kick off and had kept 15 clean sheets across all competitions.
The Millers were unable to fashion any clear openings in the first 45 minutes as a piece of individual brilliance from Hourihane saw the away side snatch the lead just before the half-hour mark.
Another superb finish doubled Swansea's lead 10 minutes later as Grimes hammered the ball into the net from outside the area.
The half-time score was harsh on Rotherham who could not do much to legislate for the visitors' sharpness in front of goal.
They were the better team during the second half, as they looked to produce an unlikely comeback.
The Millers got the goal their efforts warranted midway through the half as substitute Ladapo rose highest to head past Freddie Woodman, who was well protected by his defence for most of the afternoon.
But hopes of completing a fightback were soon dashed.
Swansea picked their moments well at the New York Stadium and restored their two-goal cushion as Jay Fulton flicked the ball past Blackman to finish a devastating counter attack.
Rotherham were almost immediately back in it when a goalmouth scramble saw them hit the crossbar but that was as close as they came before the full-time whistle sounded.
Rotherham United: Blackman; Ihiekwe, Wood (Robertson 58), Angus MacDonald; Olosunde (Giles 45), Lindsay, Shaun MacDonald (Ladapo 45), Wiles, Harding; Smith (Hirst 76), Crooks (Jozefzoon 79). Subs: Johansson, Clarke, Vickers.
Swansea City: Woodman; Bennett, Cabango, Guehi; Grimes, Roberts, Dhanda (Fulton 74), Hourihane; Bidwell; Lowe (Morris 83), Ayew. Subs: Manning, Hamer, Latibeaudiere, Cooper, Williams, Evans, Garrick.
Referee: Tony Harrington (Cleveland)
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