First-half goals from the Bosnian and the Ivorian saw the preseason title favorite take full advantage of the Reds' defeat by Chelsea to close to within three points.
Manchester City's Premier League title destiny is back in the club's own hands following a 2-0 win over Crystal Palace at Selhurst Park.
Manuel Pellegrini's men sit third, three points behind league leader Liverpool, but triumphs in the team's three remaining fixtures would almost certainly be enough to secure glory after the Anfield outfit lost to Chelsea earlier on Sunday.
The 2011-12 champion, which holds a game in hand over Liverpool and a significantly superior goal difference, wasted no time in making the Merseysiders pay for their earlier slip up – Edin Dzeko heading City in front at Selhurst Park with the game less than four minutes old.
The remainder of the first half passed by largely without incident, until Yaya Toure - making his return from injury - curled home a wonderful effort just before the interval.
Defeat brings an end to Palace's remarkable five-match winning run, while City's title tilt is well and truly back on track with games against Everton, Aston Villa and West Ham to come.
Palace's stay in the top flight looked set to be nothing more than a brief cameo for much of the campaign, but the team's resurgence under Tony Pulis has seen it emerge as a major protagonist in a season of twists and turns at both ends of the table.
However, City started Sunday's game in confident mood and swiftly moved ahead after bursting out of the blocks in south London.
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Toure sent a delightful chip into the Palace area, which Dzeko nodded home for his fifth goal in his last eight league appearances.
City initially struggled to build on its early breakthrough and rarely threatened Julian Speroni's goal prior to Toure seeing an effort blocked by Scott Dann in the box, with referee Howard Webb waving away appeals for handball.
Toure appeared in sensational form after shaking off a thigh problem, and extended his side's lead two minutes before the break.
After exchanging passes with Samir Nasri, Toure forced his way into the area before showing great composure to curl the ball around Speroni.
Palace made the early running in the second period and the in-form Jason Puncheon forced Joe Hart to punch an effort around his right-hand post.
Toure, instrumental to everything that was good about City's performance, was withdrawn after 65 minutes on his return, to be replaced by Fernandinho.
Yet the visiting side remained in control and could have moved three up when Speroni reacted well to keep out a deflected Dzeko strike.
Neither side was able to find the net as the game drew to a close, but results at Selhurst Park - where Chelsea was beaten last month - could well prove pivotal in the destination of the Premier League trophy, and it is Liverpool which faces a visit to Palace a week on Monday.