West Indies were 61-3 at lunch on the first day of a three-match series after losing the toss in overcast conditions that made life tough for their batsmen.
Surrey fast bowler Atkinson removed both West Indies captain Kraigg Brathwaite and Kirk McKenzie in an impressive return of two wickets for just two runs in five overs, including four maidens.
England captain Ben Stokes, fit to bowl following knee surgery, then had Test debutant Miklye Louis brilliantly caught one-handed in the slips by Harry Brook for 27.
Earlier, Anderson was thrust straight into the action in his 188th and final Test before retirement when Stokes won the toss and elected to field.
Stokes's decision was greeted by huge cheers from the crowd, with spectators eager to witness the last chapter of a record-breaking Test career.
Anderson has taken 700 Test wickets, the most by any fast bowler, since making his debut against Zimbabwe at Lord's in 2003.
Before play started it was the 41-year-old Anderson who presented the 26-year-old Atkinson with his England cap in a match where another Surrey player -- wicketkeeper Jamie Smith -- was also making his Test debut.
Anderson's daughters rang the five-minute bell in the Pavilion before their father led England onto the field of play to prolonged applause.
But despite a probing new-ball spell of five overs for 11 runs, Anderson was unable to dislodge either Brathwaite or fellow opener Louis.
At the other end, Chris Woakes was lofted for a dismissive legside six by the 23-year-old Louis, the first West Indies Test cricketer from St Kitts.
By contrast, it took Atkinson just two balls to make a breakthrough when Brathwaite (six) chopped on to a wide ball outside off stump.
West Indies' 34-1 became 36-2 after Kirk McKenzie's thick edge off Atkinson flew to second slip, where Zak Crawley held a sharp catch.
Louis' promising 58-ball innings then ended shortly before lunch when he fell to a sensational low catch by the diving Brook at third slip off a fine Stokes delivery that angled in and cut away to take the edge.
Anderson returned for a second spell shortly before the interval but the wicket he and the crowd craved remained elusive.
