A comprehensive loss to Ilves followed by a shock defeat last weekend to VPS had curtailed the Kuopio side's strong start to the season, and life was not about to get easier as a resurgent HJK honed into view.
The Helsinki side were on a five-match winning run in all competitions, and despite putting the visitors under plenty of pressure in the first half, the best chance of the opening 45 minutes went to KuPS' Petteri Pennanen, whose header was clawed away by Thijmen Nijhuis.
The match was played at a great tempo, but both sides were lacking that cutting edge - in the second half, a long-range drive from Georgios Kanellopoulos for the home side forced a great save from Johannes Kreidl, as the sides eventually settled for a point apiece.
KuPS have at least ended their losing run and move onto 23 points, while HJK stay fourth on 17.
The Kuopio side are now only two clear of Inter Turku at the top of the standings, thanks to the unbeaten side's 1-0 success at Jaro on Sunday, their third win in a row.
The Turku cause was given a boost after just 24 minutes when Jaro's Johan Brunell was given a straight red card for kicking out against Juuso Hamalainen.
It took the visitors until just after the hour mark to make the man advantage count, when Mamodou Sarr drove into the box from the left side and struck through a crowd and beat the goalkeeper at his near post.
It's six wins and three draws for Inter, who have two games in hand over KuPS, but will have to wait until after the international break for their first chance to overhaul them. Jaro sit 10th, without a win in four.
The leaders' fixture list will not get any easier when the league resumes on 14th June, as they will welcome Ilves, who remain third after leaving it late to secure a 2-0 victory at Gnistan.
Gnistan won the Suomen Cup match between the two 3-0 in midweek, but this was heading for a stalemate until the 87th minute, when the hosts' resistence was broken by Oiva Jukkola, who gathered a neat cutback and fired past the scrambling home defence.
The three points were sealed in added time, when Adeleke Akinyemi broke from inside his own half, played a one-two with Roope Riski and drilled home from 20 yards.
Seven points from their last three matches keeps the Lynx third, two points behind Inter and two clear of HJK. Gnistan, meanwhile, lost in the league for the first time in five matches and have dropped to eighth.
Also in the Finnish top flight, AC Oulu stayed bottom yet not only continued to improve, but heaped more misery on SJK, as the hosts equalised twice in a 2-2 draw, the second of which came in the 94th minute through Julius Korkko.
Oulu have moved onto five points, while SJK are without a league win in seven outings, but have at least moved up into fifth.
That short climb came courtesy of VPS' recent good run of form coming to an end via a 2-1 loss to Haka, for whom the victory also went against their recent record. Finally, KTP ensured they stayed a point ahead of Oulu at the bottom thanks to a 2-2 draw with Mariehamn.