The England seamer conceded a solitary run from a probing new-ball spell at Edgbaston, as the hosts reduced Australia to 83-3 at lunch.
However, the availability of England's all-time leading wicket-taker for the rest of the match is in question after the ECB confirmed he is suffering from tightness in his right calf.
Anderson injured the same muscle on July 2, while playing for Lancashire against Durham, with the problem keeping him out of action until this week.
Update: Jimmy Anderson has tightness to his right calf and will have a scan this afternoon. A further update will be given later today.— England Cricket (@englandcricket) August 1, 2019
He felt tightness at the end of his fourth over.#Ashes pic.twitter.com/bQrrECkwOf
Stuart Broad took 2-17 and Chris Woakes 1-17 in a strong start for England, although the decision to pick Anderson ahead of Sam Curran, Olly Stone and Jofra Archer – the seam trio omitted from the hosts' 14-man squad - is likely to be called into question if he is unable to return.