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South Africa suffered a 20-18 defeat by Italy in Florence on Saturday.
Wales secured a narrow last gasp win over Japan but record try scorer Williams says they have the players to beat the Springboks.
"Wales are one of the most physical teams in the world and you use that to your advantage," Williams said.
"Initially you get into an arm wrestle and you try and get ascendancy on a team.
"The scrum's gone pretty well and the driving mauls that we didn't see on the weekend were pretty good leading up to the game.
"Wales have got good enough players to go head to head with South Africa, score points and score tries and really put them under pressure.
"South Africa are hurting and this is a game Wales should win."
Replacement fly-half Sam Davies saved Wales' blushes with an 80th-minute drop-goal to beat battling Japan 33-30.
Williams, who spent three years playing for Mitsubishi Dynaboars in Japan, said Wales looked "disjointed" in their third game of the autumn series.
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"I think the players certainly should be good and capable enough to play an expansive, wide game of rugby," Williams told BBC Wales' Scrum V.
"We just didn't look comfortable ball in hand whereas Japan, a tier two side, just showed us the way in that respect.
"It's all about managing the game, we know we can play this style of rugby that Warren Gatland's been playing for quite some time - going forward and using Jamie Roberts.
"It doesn't mean we have to come away from it completely.
"We didn't do it at all on Saturday because we want to play a wide game of rugby.
"We are a professional outfit. Wales are a team which should be able to play out wide when they want to."
Williams was disappointed 18-year-old Ospreys wing Keelan Giles did not feature against Japan despite being among Wales' replacements.
"He should have started because he's a player playing with such confidence," Williams added.
"That's all you need sometimes at international level - one touch and do something right."
Shane Williams says Wales have to match South Africa physically if they are to beat the Springboks in the final Test of the autumn series.