The strong wind and difficult underfoot conditions dominated a low-scoring first half. The usually reliable David Joyce missed an early opportunity to kick 'Tarf into the lead.
Cork Constitution captain Gerry Hurley did well to open the scoring in the tenth minute, landing a testing penalty into the wind. Joyce replied in the 22nd minute and 3-3 is how it stayed up to half-time.
Despite the rain, Andy Wood's charges looked to be turning the screw in the third quarter when prolific winger Michael McGrath slid over in the right corner for his 10th try of the campaign.
But the visitors, who are known for their ability to win tight games late on, handed 'Tarf their first defeat since the opening round as Hurley coolly kicked two closing penalties in the 65th and 76th minutes.
The result, coupled with 'Belvo's victory over defending champions Lansdowne on Friday, keeps the title race wide open with Constitution now up to fourth place - ten points behind the leaders.
At the other end of the table, Garryowen showed impressive resolve to come from behind and beat Ballynahinch 18-9 in a hard-fought basement battle at Dooradoyle.
It was the Light Blues' first win of the league season and although they remain bottom of the standings, the gap between themselves and second-from-bottom 'Hinch is now seven points.
Number 10 Richie Lobb landed three penalties for the County Down club, including one from inside his own half, during a productive 13-minute spell in the third quarter.
This came after the sides had played out a scoreless first half and with Lobb then finding his kicking range, it was beginning to look glum for Garryowen.
But the Limerick outfit responded with a Jamie Gavin penalty and winger Harry McNulty's five-pointer - his third try of the season - suddenly made it a one-point game.
Roared on by the passionate home supporters, Tom Tierney's men moved ahead thanks to a converted effort from flanker Anthony Kavanagh whose back row colleague Mark Rowley was influential throughout.
A final penalty from Gavin even took the losing bonus point away from 'Hinch, as Garryowen finally ended their losing run and gave themselves a timely boost ahead of their derby visit to Young Munster in two weeks' time.
Today's other scheduled match in the top flight - Young Munster's clash with Dolphin at Musgrave Park - was postponed.
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