Debutant Harry Sloan scored to put Harlequins in control and, despite Chris Pennell's late try, deny Worcester their first Aviva Premiership win in exactly a year.
Pennell gave the away side an early lead, sending a 35-metre penalty between the posts after just three minutes.
They continued their encouraging start and soon had a numerical advantage - Quins winger Ugo Monye sent to the sin bin for deliberately not releasing a Worcester player.
Pennell struck the upright with the resulting penalty and Ryan Lamb was next to miss the target, taking over kicking duties from the full-back only to send a poor penalty wide.
Lamb was successful with his second penalty and Worcester broke the hosts' resistance on the half-hour mark, as Lemi crashed over to put them firmly in control, with Lamb adding a simple conversion.
But they couldn't preserve their clean sheet all the way to the break, as Ben Botica fired a penalty through the posts following an infringement at the breakdown.
With Conor O'Shea's words ringing in their ears Quins sharpened up after the break and forced an early penalty, which Botica confidently slotted.
Dean Ryan made a host of early second-half changes and replacement prop Euan Murray set about frustrating the Quins scrum, earning a talking-to from referee Wayne Barnes.
Barnes, who was not in the home fans' good books before half time, then dealt Worcester a blow, showing Leonardo Senatore a yellow card.
It took Quins less than a minute to bite back, rushing into the Warriors' 22 as the ball found its way to Sixways-bound Smith to cross over - but Botica missed his conversion to leave Worcester ahead.
With the Stoop roaring them on, Harlequins continued to build the pressure and good work from Sloan earned another penalty, allowing Botica to put them ahead for the first time.
And Smith was involved as Quins scored again, flicking neatly to Sloan to dot down on his Aviva Premiership debut and open up a healthy lead, with Botica adding the extras.
Pennell offered the visitors a lifeline six minutes from time, darting under the posts to score before adding the conversion himself - but they had to settle for a losing bonus point.