Hodgson grabbed a first-half try, added the conversion and landed seven penalties from eight attempts in Sunday's Aviva Premiership encounter at the Kassam Stadium.
Despite soaking up Saracens pressure for most of the match, Welsh had Sarries hanging on at the end after producing two breakaway tries from Canada wing Phil MacKenzie and full-back Tom Arscott.
Henson's boot contributed their other 13 points as they collected a losing bonus point.
The 30-year-old double Grand Slam-winning Welshman's first Premiership appearance for the newly-promoted Exiles had been delayed after he fractured his cheekbone in a pre-season match against former club Scarlets.
But Henson, called up in place of former Scotland international Gordon Ross, made his mark with an assured performance for Welsh.
They were dealt an early blow when lock Matt Corker was yellow-carded in the fourth minute as their pack desperately tried to disrupt a series of forward drives by Saracens.
But, three minutes later, they broke out of defence to take the lead, totally against the run of the early play.
Just inside the opposing half, MacKenzie kicked a loose ball deep into Saracens territory and won the race to collect and cross the line, leaving Henson a simple first conversion for his new club.
The fly-half attempted to capitalise with a penalty kick from inside his own half but his effort fell just short.
Welsh were conceding a serious number of penalties and Hodgson, after striking the post from 50 metres in the 10th minute, pulled back three points with a straightforward kick from the 22-metre line five minutes later.
The almost constant pressure of the visitors finally forced the hard-pressed Welsh defence to crack in the 18th minute when Hodgson took a short pass from scrum-half Richard Wigglesworth, stepped inside and raced over between the posts before adding the conversion.
Hodgson stretched the lead with a penalty from 48 metres but, within two minutes, Henson cancelled it out when Sarries strayed offside 40 metres from their posts.
But Hodgson struck two more penalties before half-time, with Henson pulling another back to restrict the visitors to a 19-13 lead at the interval.
Another burst through the Welsh defence by Hodgson should have resulted in a second try for Saracens but Andy Saull let the ball slip from his grasp as he stretched for the line.
Two more penalties from Hodgson increased Saracens' lead to 25-13 before Henson kicked his third penalty in the 60th minute.
But Welsh never gave up and they scored a second try when left-wing Nick Scott made a superb break from the halfway line before passing inside to full-back Arscott, who raced clear of the Saracens defence, cut inside and touched down behind the posts to leave Henson a simple conversion.
Hodgson landed his seventh penalty four minutes from time but it was not enough to deny the Exiles the hard-fought consolation point they deserved for their never-say-die efforts.
They finished the match driving the Saracens pack back towards their own line to force a penalty.
They elected to pack down and scrum-half Tyson Keats tried a burst down the short side but was dragged down just short of the line.
Saracens were forced to defend desperately but, despite conceding three penalties, they survived a series of late drives by the home forwards to hang on to their lead.
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