Saracens maintained their 100 per cent start to the Aviva Premiership season with their fifth straight victory on Saturday afternoon.
But Wasps, who ended their run of 11 successive defeats with a win over bottom-of-the-table Worcester last weekend, made them battle all the way.
England full-back Alex Goode had edged the leaders ahead with a first-half penalty, but they took a grip on the game in the second half, with flanker Will Fraser scoring their only try. Second-half replacement Owen Farrell converted before landing three late penalties to make the result safe.
Wasps captain Chris Bell replied with two second-half tries, with replacement fly-half Andy Goode landing the last-kick conversion which secured the visitors a deserved losing bonus point.
Alex Goode, switched to fly-half with Charlie Hodgson injured and Saracens' rotation policy putting Owen Farrell on the bench, kicked Saracens into a sixth-minute lead with a penalty after a breakdown infringement.
Young full-back Elliot Daly, making only his second start of the campaign after injury, showed neat footwork to escape trouble, run out of defence and put Wasps on the offensive.
Daly's 65-metre kick into touch took the visitors back into the home 22 and they stifled Saracens' attempts to counter attack with big hits from Bell and the combative back-row duo of Ashley Johnson and Nathan Hughes.
Wasps' task became even harder when lock Kearnan Myall was yellow-carded in the 26th minute for an off-the-ball challenge which left Fraser requiring treatment, but Alex Goode missed the resulting long-range penalty.
Looking to capitalise on his side's numerical advantage, Sarries' Chris Ashton chased Goode's kick to the right-hand corner but was foiled as the last-ditch outstretched boot of Wasps left wing Josh Bassett diverted the ball from his grasp.
Wasps prevented Saracens from increasing their lead during Myall's 10-minute absence and went in only 3-0 down at the interval.
Both sides switched their fly-halves for the start of the second half. Farrell's appearance, replacing Ben Ransom, saw Alex Goode revert to his normal full-back role for Sarries.
Wasps brought on Andy Goode in place of the injured Daly - the most impressive member of their back division in the first half - with Joe Carlisle moving to full-back.
Farrell missed an early chance to get on the scoresheet when he put a relatively simple 44th-minute penalty wide.
But he made amends two minutes later, starting the move which saw Alex Goode come into the three-quarter line and make the break which split the Wasps defence before he sent supporting flanker Fraser over in the left corner.
Farrell landed the touchline conversion - a much more difficult kick than the one had had just missed - before adding two more.
But Wasps hit back with a try from skipper Bell, brilliantly created by Christian Wade who is challenging Ashton for the England number 14 shirt after making his mark on the summer tour to Argentina.
Wade burst down the touchline, with his pace and footwork leaving three would-be tacklers trailing before passing out of the next tackle to send Bell over.
With 44 seconds left on the clock, Ashton was sin-binned for a deliberate knock-on and Wasps upped the pressure to salvage a point with Bell's second try, converted by Andy Goode.