Wednesday, who have made the worst start to a season in the club's 140-year history after losing their opening six games, had to soak up early pressure by a Hull side inspired by the multi-talented Jay-Jay Okocha.
The former Bolton player, signed on a free from Qatar, was behind every Hull move as he pumped in teasing crosses and peppered the Wednesday goal with long-range strikes.
Dean Marney tried his luck with a long-range strike from the edge of the area that was scooped up by keeper Lee Grant before Nigeria international Okocha picked out defender Michael Turner whose six-yard header smacked against the foot of the post.
Wednesday, pointless and propping up the Championship, went close on 29 minutes, Jeffers curling his free-kick inches wide of the target.
Okocha fired a cross from Marney over the bar and Michael Bridges was foiled by Grant, the keeper diving to his left to smother the former Leeds striker's low shot with Okocha running midfield.
Wednesday snatched the lead in spectacular fashion on 40 minutes as Jeffers turned quickly to curl the ball into the top corner from 25 yards.
Hull, always dangerous on the break, went close minutes later, Bryan Hughes heading over an Okocha corner before Grant cut out midfielder Ian Ashbee's close-range effort from Richard Garcia's cross.
In a nail-biting finish substitute Wade Small almost added a second but his low strike cannoned off the foot of the post after neat work by Frank Simek.