Hernandez's quick free-kick led to the opener from Wood, who scored for the 22nd time this season, before the playmaker's deflected effort doubled the hosts' advantage shortly after half-time.
City substitute Milan Djuric headed in a last-gasp consolation, but fifth-placed Leeds, having lost to Huddersfield and Cardiff, bounced back to consolidate their place in the play-off positions.
Garry Monk's side, containing four changes from the weekend, raced out of the blocks and Hernandez was at the heart of it, the Spaniard almost teeing up Kemar Roofe inside 10 minutes.
Although David Cotterill tested Rob Green with a long-range free-kick, Leeds dominated the first half, with Roofe and Wood going close.
The New Zealand international broke the deadlock in the 28th minute, converting Hernandez's clever through-ball from a quickly-taken free-kick that caught out the visiting defence.
Things went from bad to worse for City as 21-goal striker Tammy Abraham limped off injured, replaced by Matty Taylor in 37th minute, but the substitute brought a fine save from Green on the stroke of half-time.
Leeds were two goals to the good in the 47th minute when Hernandez's low shot from the edge of the box took a massive deflection off Aden Flint and left goalkeeper Fabian Giefer helpless.
Taylor tested Green again and Lee Tomlin saw a lob just go over the bar as City looked to get back in the game.
Leeds became complacent and only a fine performance from Green prevented City from halving the deficit, the former England international denying Djuric and Joe Bryan before Bailey Wright volleyed wide.
The hosts were aggrieved not to receive a penalty in the 68th minute when Luke Ayling, a summer signing from City, saw his shot cannon into the arm of Flint.
But City kept attacking and Cotterill and Djuric again brought brilliant saves out of Green, who clawed the latter's effort off the line with one hand, before Lee Johnson's outfit eventually got on the scoresheet after Flint volleyed against the crossbar.
It came too little too late, though, as Djuric finally beat Green with a header from a corner with what proved to be the last action of the game.