Meyer and some of his players admitted the attitude was not good enough in going down 29-15 to Ireland in the opening game of their November tour last week but they were very much up for it against England.
Their resilience was at its best when England had just scored two tries to fight back from 20-6 down to 20-20, with Twickenham rocking and Springbok lock Victor Matfield in the sinbin.
Instead of conceding further points, however, the depleted visitors drove forward and scored an all-important third try through man-of-the-match flanker Schalk Burger.
"The momentum had swung and we were up against it so it was a key time to come back and that try probably won the game for us," Meyer told reporters after South Africa made it 11 wins and a draw in 12 games against England since 2006.
"We asked for more discipline, for more attitude and we got it. Defensively we were outstanding and tactically we were much better than against Ireland."
Captain Jean de Villiers also recognised the difference seven days had made.
"Mentally, we showed up this week, that was lacking last week, we were half a second quicker in everything we did," he said.
"Defensively we were outstanding in the first half, even though we didn't get the ball and that shows attitude.
"Actually it was a pretty basic game in that the ball didn't go much beyond the 10-12 channel and sometimes in difficult conditions you just have to fight it out.
"You have to play great rugby in these conditions without the ball and we did that brilliantly today."
Meyer has won plaudits for introducing more attacking flair to the Springboks but, with an eye on the sport's biggest event next year, he made no apology for a more pragmatic approach on a soggy November Saturday in London.
"We want to evolve this team, we want to play with the ball in the hand but sometimes in a game like this you have to grind out the win," he said.
"That's winning rugby - that's World Cup-winning rugby."