Frank Lampard's Derby side needed a victory to guarantee sixth place and they could start celebrating after two goals in three minutes in the second half from Mason Bennett and Harry Wilson settled the jitters.
West Brom, already assured of fourth spot, had equalised just after halftime through Stefan Johansen after Derby had led at the interval through Martyn Waghorn's header.
Middlesbrough did their part, winning 2-1 away at Rotherham United while Bristol City, who also still had a chance of making the top six if results went their way, drew 1-1 at Hull City.
Norwich City were confirmed as champions after winning 2-1 away at fifth-placed Aston Villa.
Sheffield United, who finished runners-up and also gained automatic promotion to the Premier League, ended with a 2-2 draw at Stoke City.
Third-placed Leeds United, who for so long seemed destined to go up automatically before a late-season slump, finished their regular season with a surprise 3-2 defeat by bottom club Ipswich Town.
Leeds will face Derby in the two-legged playoff semi-finals which begin next weekend, with West Bromwich Albion up against Midlands rivals Aston Villa.
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