Leicester fly-half George Ford missed two crucial drop goals as Exeter won a brilliant match 30-28 at Welford Road to beat the Tigers for the first time.
The Chiefs led 23-15 at the break and ran in tries from Sireli Naqelevuki, Matt Jess and Tom Johnson, all converted by Ignacio Mieres who also kicked three penalties.
Leicester threw the kitchen sink at their opponents in a fantastic finale and looked to have secured it only for Ford to miss a straight-forward drop goal wide of the upright.
Exeter were hanging on for dear life still with their two-point advantage as the last play of the game arrived with the Tigers camped on the Chiefs' 22.
And one last attempt at a drop goal from Ford from 30 metres, with the Chiefs players trying to charge it down, went wide and Exeter secured a famous win.
Leicester had tries from Niall Morris (2) and Thomas Waldrom, while Billy Twelvetrees landed two conversion and two penlaties with Ford notching one drop goal but it was not enough.
An immaculate seven-out-of-seven kicking display by Nick Evans enabled Harlequins to secure victory as they edged past London Irish 29-24.
The former All Blacks fly-half kicked five penalties and converted tries by James Johnston and England winger Ugo Monye.
The early kick-off at Twickenham meant Johnston's seventh minute effort was the first try of the new season.
Irish responded with two excellent tries from former England winger Topsy Ojo, with full-back Tom Homer kicking four penalties and a conversion to have the consolation of a bonus point.
Saracens' return to Twickenham ended on a sour note as they were dealt an opening-day 20-15 defeat by Wasps.
The defending champions, back at the game's headquarters for the first time since their title win over Leicester in May, allowed Wasps to come from behind and take the win with a late Tom Varndell try.
Christian Wade also crossed for Wasps, Nicky Robinson converting both and adding two vital penalties.
Sarries' points came from the boots of Charlie Hodgson (2), Owen Farrell (2) and Adam Powell.
Worcester resumed life in the top flight with a hard earned 17-12 win over a spirited Sale side at Sixways.
The Warriors scored the only two tries of the game and should have won more comfortably with Sale only having 12 points from the boot of Nick Macleod to show for their efforts.
Sale were leading 6-0 but on the stroke of half-time Worcester scored the first try of the game.
A long pass was picked up by the elusive Claassens for the full-back to evade Joe Ward's tackle and send Miles Benjamin over in the corner for the try and Sale also conceded a penalty try.
It was the Sam Vesty show at Kingston Park as the Bath fly-half rattled up 17 points from four penalties, a drop goal and a conversion and engineered the game's only try as his side rumbled to a comfortable 22-9 Premiership victory over Newcastle.
Bath's pack dominated the game and Newcastle did themselves no favours by conceding lots of penalties, mainly at the breakdown, and an early try from Matt Carraro from which they never really recovered.
Jimmy Gopperth landed three first-half penalties as the hosts trailed 1309 at the interval before Bath pulled clear.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.