Warriors narrowed the deficit when Mieres kicked a penalty from 25 metres out and the home side kept coming as the match entered its final quarter.
Ryan's side kept pushing forward and retook the lead with a sensational try from Mieres with ten minutes remaining.
The fly-half started the move minutes earlier as his high kick was caught by Josh Drauniniu, who set Matavesi on his way.
Irish defended brilliantly but Warriors went through several phases of play as they moved towards the line.
When the ball did break, Matavesi showed produced dummied a pass before eventually setting Mieres on his way to dive over in the corner.
The try set-up a nervy finale and Irish went ahead again with three minutes remaining as Humphrey added a penalty.
Warriors continued to attack as they looked to claim a vital home victory but their final attack was ended by Irish as the full-time whistle was blown.
5m: Mieres pen 3-0
14m: Humphreys pen 3-3
17m: Lemi try 8-3
18m: Mieres con 10-3
38m: Yarde try 10-8
39m: Humphreys con 10-10
47m: Yarde try 10-15
48m: Humphreys con 10-17
60m: Mieres pen 13-17
70m: Mieres try 18-17
77m: Humphrey pen 18-20
Warriors: 01 Paul Andrew, 02 Ed Shervington, 03 Euan Murray (Andress 54), 04 Mike Williams, 05 Chris Jones (Schofield 54), 06 Jonathan Thomas (c), 07 Sam Betty (Abbott 67), 08 Semisi Taulava, 09 Paul Hodgson (Su'a 49), 10 Ignacio Mieres (Gray 71), 11 David Lemi, 12 Josh Matavesi, 13 Ravai Fatiaki, 14 Josh Drauniniu, 15 Chris Pennell
Replacements: 16 Nick Seymour, 17 Ofa Fainga'anuku, 18 John Andress, 19 Dean Schofield, 20 Jake Abbott, 21 Jeremy Su'a, 22 Danny Gray, 23 Jon Clarke