Former England fly-half Hodgson went from hero to villain as the battle of the Red Rose number 10s past and present ended in stalemate.
After replacing the woefully off-colour Owen Farrell early in the second half Hodgson's kicking - both from the tee and in open play - dragged Saracens back into the game.
However, after kicking two penalties in quick succession to level proceedings, the 31-year-old was off target with a last-gasp drop goal in front of the posts.
Another England fly-half, Toby Flood, kicked the three penalties that had seemingly put Leicester on course for victory but the Tigers pivot was also off-target with a drop-goal attempt with the last kick of the game as the points were shared.
The place-kicking battle started early, with Flood successful with two penalties inside the first six minutes.
Sarries barely got out of their own half early on but slowly came into the match and could have reduced the deficit on 10 minutes.
But in a sign of what was to follow in a dismal first half for Farrell, making his first start of the season, the 20-year-old dragged his effort wide - the first of four misses from five attempts.
Leicester skipper Geordan Murphy was forced off through injury after 14 minutes, replaced by Matt Smith, before Farrell failed to take advantage with his next penalty attempt - dragging his effort off target from 40 metres.
The Tigers slowly took a grip on the game and enjoyed an impressive spell of possession, Vereniki Goneva and Scott Hamilton nearly linking up to produce the first try but for the timely intervention of Alex Goode on the left wing.
Despite sustained pressure they had to settle for a penalty, Flood extending the lead to nine with his third success on the half-hour mark.
Farrell finally got himself off the mark with his fourth penalty attempt on 34 minutes but he was wayward again with the last kick of the first half to leave the margin at 9-3.
Sarries kept the faith with their misfiring fly-half in the early stages of the second half but Hodgson joined the fray in the 51st minute and seconds later succeeded where Farrell had failed.
The former Sale number 10 - who retired from international duty in the summer - kicked Sarries to victory against his old club last week and he found his range immediately after Tigers were penalised for coming in at the side.
The scores were level before the hour mark when Hodgson made it two from two. Julian Salvi did not roll away quickly enough and the 31-year-old duly slotted the penalty to set up a grandstand finish.
Leicester had the next chance to restore their lead on 68 minutes but Flood pulled his kickable penalty attempt wide for his first miss of the day at a most inopportune moment.
Sarries wasted a chance on the counter-attack after some quick thinking by Goode, Richard Wigglesworth knocking on with a gap looking to have opened up.
A Saracens turnover and a kick ahead from Hodgson forced Leicester to concede a line-out within metres of their line heading into the last five minutes.
Safe line-out ball allowed Sarries to set-up the replacement fly-half with a drop-goal attempt in front of the posts but Hodgson sliced it wide.
Leicester got themselves down the other end of the field to give Flood his chance to be the hero but his effort was just wide as the points were shared.
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