Jennings exited for 17, the only wicket to fall in a session that saw England reach lunch on 67 for one against a Proteas attack missing Vernon Philander and Chris Morris after both pacemen were ruled out with lower back strains.
England captain Joe Root won the toss and batted in initially overcast conditions, just as he'd done in a 239-run win in the third Test at The Oval.
Jennings, under pressure for his place after just one fifty in nine Test innings since a century on debut against India in Mumbai in December, was almost out for four.
But fast bowler Kagiso Rabada could not quite hold on to a diving caught and bowled chance following the Durhan left- hander's inside edge onto the pad.
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Jennings was out though when, getting only half forward to Duanne Olivier, he was caught behind by wicket-keeper Quinton de Kock, a former team-mate in the XI at Johannesburg's King Edward VII school.
Westley, in just his second Test, walked out to join Essex colleague Cook with England 35 for one in the 13th over.
Cook, England's all-time leading Test run-scorer, looked in good touch.
The former England captain drove fast bowler Morne Morkel straight for four and the left-handed opener struck another well-timed shot past Olivier.
Westley, fresh from his second-innings fifty at The Oval, almost played on to Rabada for one.
However, he subsequently hit four fours -- the best a back-foot drive through the covers off medium-pacer de Bruyn.
Before play, a presentation was made to James Anderson after the Pavilion End at Old Trafford, his Lancashire home ground, was officially renamed the James Anderson End in honour of England's all-time leading Test wicket-taker.