In a match that swayed back and forth for the first hour, Fernandinho gave the Blues a first-half lead that was cancelled out on half-time by Wilfried Bony.
But a determined City added a couple of goals just before and past the hour-mark from Yaya Toure and Aleks Kolarov to seal three points and record a first win in Swansea for 30 years.
There was still time for the impressive Bony to pull one back in added time but it was too little, too late for the hosts.
A rain-swept Liberty Stadium wasn’t the most auspicious of settings to begin 2014 for the Blues. The early afternoon kick-off at one of the furthest Premier League destinations possible was a tough ask for the City fans who made the journey to South Wales, but a fourth successive win on the road would make the trip more than worthwhile.
With no David Silva, Manuel Pellegrini opted to go 4-4-2 with Alvaro Negredo and Edin Dzeko in tandem up front and it was the Blues who began the brighter with Dzeko whistling a low drive inches wide after four minutes.
At the other end, Bony responded with a sizzling low shot that shaved Joe Hart’s post and the powerful Ivorian would be a constant thorn for the City defence throughout the game.
But it was the visitors who struck first when Samir Nasri’s corner was half-cleared and Fernandinho drilled the ball through the crowded box and into the net with just 14 minutes on the clock – the first goal the Blues have ever scored at The Liberty Stadium.
City failed to kick on or take the game by the scruff of the neck, despite Dzeko having a couple of chances to increase the lead and were ultimately made to pay.
The hosts really came to life in the final 15 minutes of the half and Bony again served notice of his intentions as he whistled another 20-yard howitzer inches wide on 44 minutes – but two minutes later Bony finally found the target, beating Hart with a header from a Jonathan De Guzman cross.
Replays proved he was offside but it mattered little with the goal already given – was this to be another miserable trip to South Wales after all? Yaya Toure, however, had different ideas.
The Blues re-took the lead 12 minutes after the re-start with a goal borne out of determination as a Navas cross was scrambled clear to the edge of the Swansea box. Pablo Zabaleta won the loose ball and Yaya took over, moving past one challenge before hitting a rasping deflected drive past Tremmel for his 12th of the campaign.
There was better to come eight minutes later when Kolarov powered forward on the counter-attack before cutting inside the box and firing a powerful drive past Tremmel with his right-foot – a collector’s item! It also gave City vital breathing space
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It was needed, too, as the impressive Bony scored in stoppage time to reduce the arrears but the Blues played out the remaining seconds comfortably to record a fifth straight league win and kick-off 2014 in style.
