Sarries recorded a third consecutive win in the defence of their title in convincing fashion.
Hodgson scored a try, three penalties and three conversions, while back-row forward Ernst Joubert claimed two tries as Saracens made light of their own problems with injuries and World Cup absences.
Saracens underlined their dominance with a three-try burst early in the first half and had too much power and experience for the hard-working Tigers in what was a one-sided re-match of last season's final.
The result leaves Leicester, who were without 16 first-team squad players, with just one win from their opening four matches, while Saracens' third consecutive win came despite having eight of their top players away on World Cup duty.
Saracens began the match in ominous fashion, with Hodgson kicking three early penalties to one by Twelvetrees as the visitors opened up a 9-3 lead.
The Premiership's all-time top scorer then grabbed a nicely worked try, which he converted to make it 16-3.
At that point, Leicester's under-strength side were acquitting themselves well but struggling to cross the advantage line, relying heavily on some smart clearing kicks by young fly-half George Ford to relieve the pressure.
Twelvetrees did notch his second penalty just before the half-hour mark, but a sudden rash of missed tackles cost his side dear moments later, as Saracens back-rower Ernst Joubert ran 35 metres through some flimsy defence to stretch the lead to 21-6, with Hodgson adding the extras.
The Tigers grabbed a nicely worked try just before the break through winger Niall Morris but still went into the break 23-11 down.
The woe continued after the break, as Saracens put the result beyond any real doubt before the hour mark was up.
Inside centre Owen Farrell strolled through untouched just a minute after the re-start, Tigers defenders looking at each other rather than putting in the key tackles.
Hooker Jamie George scored on the end of an overlap and Joubert picked up his second before the three-quarter mark was reached, putting his side well in command of what was rapidly turning into a one-sided affair.
Amid his team's disappointing defending, Julian Salvi did pick up a try for Leicester following some dynamic work by replacement Mathew Tait, with Twelvetrees nailing the tricky conversion.
By the time Hodgson was replaced just after the hour, with 20 points to his name, his side were 40-18 ahead and cruising.
To their credit, the Tigers never gave in and looked for every opportunity to ask questions of Saracens, but the visitors were well organised in defence and always threatening on attack.
Saracens' sixth try came with just four minutes left, Brad Barritt scoring under posts and Farrell adding the conversion to underline their dominance.
Tigers fans did have something to cheer about when Ben Woods scored a consolation try with a couple of minutes remaining and Twelvetrees knocked over the difficult conversion.
Farrell rubbed some salt into the Tigers' wounds though by kicking a very late penalty, the last act of the game making it a half century a points for the visitors.
Well before time, Saracens looked satisfied with their afternoon's work, which included a useful bonus point.
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.