Airline Captain reported; while following ATC control instructions; complying with a TCAS RA advisory resulted in a NMAC with a large transport aircraft opposite direction.

Narrative

Aircraft X During the approach phase into DTW; we were left high on a downwind leg for 21L. At around 10;000 ft. we given a descent to 3;000 ft. at a speed of 210 kts. This required a high rate of descent. I selected the Auto pilot (AP) off so I could use full speedbrakes. At about 5;000 ft. ATC turned us into a base leg heading of 270. While turning through a heading of 300; at about 4;000 ft; TCAS identified a target at our 12 o'clock; same altitude. I announced 'TCAS I have control'; and stowed the speedbrakes. We identified Aircraft Y 12 o'clock opposite direction. TCAS annunciated 'LEVEL OFF; LEVEL OFF'. I verbalized the TCAS memory items and reduced VS to the green range depicted. Simultaneously ATC told us to fly a heading of 300 and 'level off there'. The First Officer (FO) replied 'TCAS RA'. We both observed Aircraft Y fly beneath us in a right hand turn. TCAS indicated -01 and -02. Once clear on conflict; we complied with ATC instructions and were vectored for a visual approach to 21L; the remainder was uneventful.