With most of the action played between both twenty-twos in the opening period, Leinster's defence was impenetrable with New Zealander Ben Gissing and his second row partner, and skipper for the day, Leo Cullen impressing.
Leinster lacked a cutting edge in attack and trailed at the interval 3-0. Leinster bounced back to edge into a three point lead after two David McAllister penalties within the first 15 minutes of the second half.
The visitors' lead was short lived though and Worcester regained their advantage with a try in the corner in the 58th minute to give them an 8-6 lead.
Coach Declan Kidney introduced Leinster's Young Player of the Year from last season Niall Ronan, Ireland international Victor Costello and recent signing prop Ricky Nebbett on the hour as he bid to maintain his side's winning run with Des Dillon number eight outstanding.
And hooker Gavin Hickie was on hand to touch down in the corner moments later when he took a Gissing lineout and after a clever one-two with scrum-half Brian O'Riordan dived into the corner.
McAllister's conversion fell wide of the upright and Worcester tied the game at 11-11 with another penalty to ensure a tense finale.
It was Leinster's final pre-season game of the season before their Celtic League opener against the Cardiff Blues next Sunday in Donnybrook (5.15pm).
Tickets are on sale now from the Spar in Donnybrook and from the Leinster Branch from Monday (01-2693224).