After a 30-minute delay to the kick-off, four tries in the opening 18 minutes owed much to the poor defence of both sides rather than any real cutting edge.
Tom Biggs opened the scoring for Leeds after seven minutes after the ball had gone through 12 phases of play.
Space was created down the left touchline by the quick hands of Gordon Ross and Alix Popham, who worked an opening for the pacy 20-year-old winger to scamper in at the corner. Ross was unable to convert.
Worcester responded with a try of their own on 14 minutes after Tim Stimpson, making his first start for the Tykes, lost the ball in the tackle.
The ball was shipped left to skipper Pat Sanderson who threw a delightfully weighted miss pass to winger Ben Hinshelwood to scream in from 40 metres. Fly-half James Brown converted.
John Dunbar hit back immediately for the home side when he took advantage of Ben Gollings' and Matt Powell's decision to step aside and wave him through at the side of a ruck. Ross converted to make it 12-7 to the Tykes.
Thomas Lombard scored for the Warriors two minutes later after the Tykes made a mess of the kick-off, Hinshelwood providing the telling pass to the Frenchman. Brown missed the conversion.
The rest of the half settled down into something like normality, with both sides tightening up their defences.
Two Gordon Ross penalties meant the sides turned round with the home side ahead 18-12.
Ross kicked two early second half penalties for the Tykes to edge them further ahead at 24-12.
The crowd gave England international Balshaw a generous reception when he came off the bench on 61 minutes to make his home debut for the Tykes after a long lay-off with a groin injury.
Balshaw made an immediate impact when Tim Stimpson created space for him down the right.
Balshaw turned on the afterburner and it took a thunderous tackle from South African full-back Thinus Delport to stop him five yards short of the line.
A late converted try by 18-stone replacement winger Sione Kepu gained Worcester a deserved bonus point.
But Leeds held on to take them further clear of trouble at the bottom of the table.
For Leeds Tykes:Tries: Biggs, DunbarCon: Ross Pens: Ross 4
For Worcester: Tries: Hinshelwood, Lombard, KepuCons: Brown 2