Jamieson is bidding to claim his second DP World Tour title.
The 34-year-old went into the day with a three-shot lead, having produced a course-record 63 on Friday, but struggled on the front nine - carding two birdies and three bogeys.
However, he bounced back with a hat-trick of birdies at the 11th, 12th and 13th to sign for a 70 and join home favourite Strydom on 15 under par.
Strydom, meanwhile, made a huge move on Saturday, carding an eagle, eight birdies and a single bogey to equal Jamieson's course record and earn a share of the lead.
The leading pair are two clear of Englishman Dale Whitnell and South Africans Dean Burmester and Oliver Bekker in a tie for third.
Jamieson is looking to make it a South African double, having won his only DP World Tour title so far there at the Nelson Mandela Championship 10 years ago.
Strydom has yet to win on the DP World Tour and vowed to do nothing differently on Sunday as he goes in search of a first crown.
He said: "I'm just doing the same as what I've been doing every day.
"I'll play golf - if it comes out, it comes out. If it doesn't, you've still got next week to go."