Midfielder Baba Mahama was the hero of the day after he calmly slotted in a pass from teammate Jackson Owusu in the first-half as Kotoko made it two wins in a row.
Kotoko coach Steve Polack maintained the team that defeated title holders Wa All Stars over the weekend in Kumasi while the league's most dangerous man Nicholas Gyan led the attack of Dwarfs.
The hosts had the first opportunity to grab the opener by the fourth minute after Kotoko striker Obed Owusu brought down Isaac Kwain to receive the first booking of the day. Dwarfs wasted the resulting free-kick before goalkeeper Felix Annan made another timely intervention two minutes later to save Kotoko from going behind.
The Porcupine Warriors were handed a perfect opportunity to grab the opener on 13th minute when Emmanuel Gyamfi played Yakubu Mohammed through but the latter surprisingly shot wide and missed another cross from Gyamfi on 25th minute.
However, the visitors finally found the back of the net by the 31st minute to the delight of the traveling supporters. Gyamfi played through Jackson, who pulled it back for Mahama and the former Techiman City star made no mistake with his final touch to beat goalkeeper Michael Abu.
After the break, Gyan threatened Kotoko's box on several occasions but the league's topscorer could not score his eleventh goal of the campaign in all the attempts.
Kwain's cross was blocked by Amos Frimpong but the right-back managed to get his second cross in only to be headed wide by Gyan.
With 15 minutes remaining, Kotoko resorted to counterattack as coach Polack brought on speedster Ashittey Ollenu for Yakubu and Michael Akuffo also coming on for Obed.
On 83rd minute, Kotoko's substitution nearly fetched another goal when Awal Mohammed saw his powerful drive tipped to the corner-kick by Abu.
Gyan had the last opportunity to level the scoreline but he somehow missed his steps and the visitors recovered.
Kotoko have moved one place up to fourth position with 32 points, eight points behind leaders Wafa while Dwarfs have dropped to sixth position with 27 points.
Kotoko will switch their attention to the President Cup against Hearts on Sunday in Kumasi.