Anderson, who removed opener Azhar Ali for nought in the first session, came back strongly to trap Younis with an incoming delivery to leave Pakistan, who won the toss and decided to bat, struggling on a grassless Sharjah stadium pitch.
At the break Pakistan skipper Misbah-ul-Haq was unbeaten on 26 and with him Sarfraz Ahmed on 19 not out.
England bowlers kept a tight length as Stuart Broad bowled seven maidens out of his eight overs while Anderson had figures of ten overs, six maiden with 8-2.
Shoaib Malik fell caught behind off paceman Stuart Broad for 38 and Asad Shafiq was dismissed for just five.
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Broad put pressure on Pakistan batting by claiming his first wicket in the third over after lunch as Malik edge one to wicketkeeper Jonny Bairstow.
Younis, who survived a confident caught behind appeal off Broad on 21, became Anderson's 422nd wicket in his 110th Test.
Anderson is now eighth on the all time leading Test wicket takers, leaving South African paceman Shaun Pollock (421 wickets) behind.
Malik, who hit a career-best 245 in the drawn first Test in Abu Dhabi, successfully challenged Australian umpire Bruce Oxenford's leg-before decision off spinner Moeen Ali when he was on 22.
Pakistan lost opener Ali, who missed the first Test with a foot injury and the second due to the death of his mother-in-law, in the third over when he edged Anderson to Bairstow without scoring.
Mohammad Hafeez swept Moeen Ali's first delivery to the boundary but miscued a pull shot and was caught in the deep by Broad for 27.
Pakistan made two changes from the side which won the second Test in Dubai for a 1-0 lead, bringing in Ali and paceman Rahat Ali for Shan Masood and injured Imran Khan.