Despite being without a win in eight in all competitions prior to Saturday's match, the hosts struck twice in the first half to halt Derby's seven-match unbeaten league streak.
Kit Symons' side were rewarded for a superb start when Bodurov gave them the lead with his maiden Fulham goal midway through the first half.
Woodrow then added a second on the stroke of half-time, and although the visitors had plenty of possession, they never looked likely to pull one back.
Derby's blushes were spared somewhat as second-placed Middlesbrough missed out on the chance to go top after losing 2-0 at Sheffield Wednesday.
Second-half goals from Atdhe Nuhiu and Will Keane sealed a first triumph at Hillsborough for Stuart Gray's side since Boxing Day.
Elsewhere, Leeds United suffered their second consecutive defeat as they were edged out 3-2 by Watford at Elland Road, with Matej Vydra's second-half double capping a superb comeback for the visitors - now just a point behind Middlesbrough.
After going two down within 20 minutes, Watford fought back to level before Vydra snatched the points with just under 10 minutes remaining.
Dougie Freedman's fine start as Nottingham Forest manager continued as his side beat Reading 3-0 at the Madejski Stadium – with the Scot having now won five of his six matches in charge.
Blackpool's dismal form continued with a 3-1 loss to fellow strugglers Wigan Athletic at Bloomfield Road, while Rotherham United came from behind to move six points clear of the relegation zone with a 2-1 victory over Millwall.
Brentford squandered the opportunity to leap into fourth place as they succumbed 1-0 to 10-man Birmingham City, with Wolves now just a point behind Mark Warburton's side after their 1-0 victory over 10-man Cardiff City, who had Peter Whittingham sent off for two bookable offences.
Tony Watt's brace helped Charlton to a 3-0 win over Huddersfield Town, whose manager Chris Powell endured a nightmare return to his former club.
Zach Clough's sixth goal of the campaign was enough for Bolton to overcome Brighton 1-0, while in Saturday's other fixture, Blackburn held Bournemouth to a goalless draw.
