Nick Evans kicked two penalties to Jimmy Gopperth's one before Wasps grabbed the game's first try as Jake Cooper-Woolley bundled his way over the line.
But the lead was short lived as home fly-half Evans started and finished off a superb move as Harlequins headed into the break 13-11 ahead.
Harlequins moved further ahead shortly after the break as George Lowe went over, with Evans keeping Wasps at bay with a series of penalties.
Daly did touch down with three minutes remaining to bring Wasps to within five points of their hosts, but Harlequins held on for the win.
After some early adventure from Harlequins, Wasps grew into the game and after two lineout successes a powerful rolling maul almost had the visitors over but for a knock on, with referee Luke Pearce going back for a penalty which Gopperth sent over for a sixth-minute lead.
But that advantage was short lived as just moments later Evans split the uprights at the other end of the pitch.
And shortly afterwards the home side were in front as a clever kick through from Lowe left Christian Wade under intense pressure from Marland Yarde and Lowe and Quins forced the penalty which fly-half Evans duly converted.
But this topsy-turvy match swung back in Wasps' favour as prop Cooper-Woolley bundled his way over in the corner on 17 minutes after a strong break from Daly.
Gopperth sent his touchline conversion wide and on 26 minutes Evans showed him how it is done as the Kiwi started and finished a superb try for the home side.
Evans' initial chip over the top put Yarde into space, he found Karl Dickson and the scrum-half's superbly weighted kick was collected by the home side's No.10 who added the extras for a 13-8 lead.
A Gopperth three-pointer reduced the arrears and after Yarde spilled the ball just three metres away from Wasps' tryline, Evans then hit the post with a penalty of his own.
Yarde was a constant threat but he still couldn't find a first-half try as he was hauled down just metres short again, Gopperth missing a penalty at the other end from 30 metres out as the hosts went in at half-time 13-11 ahead.
Harelquins didn't wait long after the restart to get on the scoreboard again as a neat offload from Evans saw Lowe dot down, the Kiwi fly-half adding the extras.
But Gopperth kept Wasps in the game with a penalty right in front of the posts and the visitors were painfully close to crashing over but Ashley Johnson was just short after a break from Rob Miller.
With time ticking down Evans slotted two three-pointers to push the home side 12 points clear.
But Wasps refused to lie down and Wade showed lightning footwork before a short pass inside saw Daly finish from 35m out.
Ruaridh Jackson added the extras and Wasps pushed for another score but Joe Marler secured a turnover at the death and Mike Brown was bundled into touch to bring on the final whistle, much to the home fans' relief.
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