Steyn (groin) failed to finish the first over of the West Indies' second innings at Centurion on Friday, after the Proteas bowled the tourists out for 201 earlier in the day.
Philander collected five of South Africa's 11 wickets for the day - with Denesh Ramdin's men 76-2 in their second innings - but pulled up with a sore hamstring.
South Africa's team manager Mohammed Moosajee confirmed the pair will be fit to try and complete an innings victory for the hosts - as the Proteas maintain a 275-run lead.
"Both Dale and Vernon experienced some tightness...understandably," Moosajee said.
"The guys have bowled a team out in 60 overs. They each have bowled about 15 overs. It was more of a precaution that they came off.
"They will get treatment overnight and I'm sure they will be fine tomorrow morning."
Moosajee said the pair were already undergoing treatment throughout the day, as the Proteas dominated in the first of three Tests.
"The outfield has been quite heavy so it was just about taking them off, ice baths, getting them on the physio's bench," Moosajee said.
The manager also claimed their absence from the Test arena since early August had led to some rustiness among the bowlers.
"It's very individualised. It's about body being conditioned to bowling those kind of overs. The intensity of bowling a side also affects you," Moosajee said.
"The reality is we haven't played Test cricket for about five months."