The Ireland international scored the only try of a pulsating match at the Gnoll on Sunday to leave a star-studded Ospreys region winless after the opening two rounds of the Heineken Cup.
Referee Joel Jutge ensured plenty of goal-kicking practice for both sides, with hometown star Gavin Henson slotting six penalty goals and opposite number Ronan O'Gara converting five.
It was the first sellout crowd at the Gnoll for 10 years, and they were on the edge of their seats throughout as neither side got further ahead than five points in a hard-fought Pool 4 fixture.
Munster skipper and man of the match Paul O'Connell was a relieved man after the match.
"We've come in for a bit of criticism recently, so it was nice to get a victory over a good side," he said. "We expected a big match and we got it, but our defence was the key on the day. The Ospreys are going to become a very good team, so it was good to get the win away from home."
Opposite number Barry Williams added: "They're a bit more street-wise and that showed in the end - they dogged it out a bit better than us.
"We played some good stuff - especially in the second half - but we have to take our hats off to their defence."
The Ospreys led 12-9 at halftime, but the second half was barely two minutes old when the first try arrived. Stringer scampered around the blindside of a close-range scrum to score without a hand being laid on him.
A great tackle from Wales centre Sonny Parker set up another penalty attempt for Henson, and he made no mistake as the Ospreys regained the lead of a see-saw match.
O'Gara's fourth penalty goal gave his side a 17-15 lead, and another attempt hit the upright but fell on the right side of the crossbar to give the Irishmen a crucial five-point lead.
A terrific break from Ospreys scrum-half Jason Spice set up the opportunity for Henson's sixth goal, but the Neath-Swansea region couldn't breach a rock-hard Munster defence, despite some great work from Henson and scrum-half Jason Spice.
Ospreys: (12) 18 Pens: Henson 6.
Munster: (9) 20 Try: Stringer. Pens: O'Gara 5. Teams:
Neath Swansea Ospreys:
A Durston; R Mustoe, S Parker, E Seveali'i, S Williams; G Henson, J Spice; D Jones, B Williams (capt), A Jones, A Newman, B Cockbain, J Bater, S Tandy, R Jones.
Replacements: M Davies, P James, L Tait, L Bateman, R Pugh, A Williams, M Jones.
C Cullen; J Kelly, S Payne, R Henderson, A Horgan; R O'Gara, P Stringer; M Horan, F Sheahan, J Hayes, D O'Callaghan, P O'Connell, J Williams, D Wallace, A Foley (capt).
Replacements: J Flannery, G McIlwham, T Hogan, A Quinlan, M Prendergast, P Burke, M Lawlor.