Having picked up an impressive point against leaders Inter Turku last time out, KTP travelled to Valkeakoski to face Haka, who themselves were three matches without a win.
But any hopes of KTP carrying any momentum into this game looked to be dashed when Jean-Pierre Da Sylva put the home side ahead from the penalty spot midway through the first half.
However, the visitors' response was almost immediate - two minutes later Rangel slotted home the equaliser after being played through by Joni Makela.
In the second half, it was a case of deja vu for both sides, as once again it was Da Sylva who put Haka ahead, this time just six minutes after the restart, but once more it took just two minutes for KTP to get back on level terms as Nathaniel Tahmbi made it 2-2.
Just past the hour mark, the Kotka side went in front for the first time when Assan Seck sent Atomu Tanaka on his way into the penalty area before cutting inside and finding the bottom corner.
3-2 was how it stayed as Haka drop to 10th and remain without a home league win since May, while KTP now have 14 points, two fewer than their opponents after their third league victory this season.
However, KTP will remain bottom of the table for another week, as AC Oulu's recent successful run continues, picking up a third win in five Veikkausliiga matches by beating Mariehamn 1-0 on Aland.
A nervy contest saw just two shots on target throughout the 90 minutes, both going to the visitors, and the more crucial of the two efforts arrived five minutes from time.
Niklas Jokelainen battled hard to retain possession in midfield before finding Tuomas Kaukua on the left wing. His dinked cross was met a few yards out by Momodou Fadera, who made no mistake with his header.
The loss ends a run of three consecutive draws for Mariehamn, who sit eighth and without a win in five and are now two points clear of Oulu, who themselves retain a one-point advantage over KTP.
With those two away wins on Saturday, every team in the Veikkausliiga still harbours ambitions of reaching the top six and the Championship Round, as only six points separate KTP and sixth-placed VPS, who drew 2-2 with Jaro on Friday.
After a goalless first half, VPS gave themselves a chance of getting back to winning ways when Tristan Dekker put them ahead, only for Adam Vidjeskog to peg them back just after the hour mark.
Michael Ogungbaro then put the home side ahead on 68 minutes, only for Maissa Fall to salvage VPS a point three minutes later.
Jaro sit ninth, a point behind Mariehamn and without a win in four, while the side from Vaasa continue to look over their shoulder as they slip to seven games without a win.
VPS will lose their place in the top six tomorrow if Gnistan can get another positive result against Helsinki rivals HJK. Also on Sunday, Inter Turku will look to preserve their unbeaten league season against a resurgent SJK.
KuPS and Ilves, both involved in European action, do not play this weekend.