Saha helped himself to a double to take his tally for the season to 13. But that only tells half the story. Twelve of the goals have come in his last 18 appearances with seven in the last eight matches.
It is a run of form that is keeping leading scorer Ruud van Nistelrooy on the bench as the Dutchman started his fourth successive match among the substitutes at The Hawthorns.
United were grateful to Saha for his two goals as they did not create very many other chances on the way to a fifth successive win. Wayne Rooney was subdued by his normal standards as Albion made them battle all the way for their victory.
United had to withstand a late scare when Nathan Ellington pulled a goal back for Albion 13 minutes from time but it was too little too late for Bryan Robson's side.
Albion had enough chances in the first half to take something from the game only to be frustrated by goalkeeper Edwin Van der Sar as they crashed to their fourth defeat in five games - collecting a possible one point from 15.
After making the early running when Curtis Davies flashed a fourth minute header just wide, Albion were made to pay for some slack defensive play when United took the lead in what was really their first attack of note.
When former Albion loanee Kieran Richardson whipped in a left-wing cross, Steve Watson's misplaced clearance handed United a corner. Ryan Giggs floated over a cross that picked out the unmarked Saha who buried his header from ten yards after easily escaping the attentions of Martin Albrechtsen.
Saha's strike looked set to signal the start of a United onslaught. But that did not materialise and United could consider themselves lucky to get to half-time still in the lead as Albion launched a determined bid to get back on to level terms.
It was only the heroics of Van der Sar that ensured United took their lead into the interval. The Dutchman pulled off two stunning saves in the space of 120 seconds to frustrate determined Albion.
First he pushed a goalbound 20-yard free-kick from Diomansy Kamara around the post in the 36th minute before frustrating Davies by palming away his header following a corner from Jonathan Greening.
Not to be outdone, Albion goalkeeper Tomasz Kuszczak then produced a stunning save of his own five minutes before the interval when he pushed a rising drive from Giggs over the bar.
It signalled the start of a spell of intense United pressure at the start of the second half that eventually led to Saha making the game safe.
After Cristiano Ronaldo and Rooney had both gone close, Saha struck with another piece of smart finishing. Giggs released Ronaldo who in turn flicked the ball into the path of Saha.
The former Fulham striker was again unmarked and he had time to look up and steer his shot past Kuszczak to end Albion's resistance.
United looked set to cruise to victory after Saha's second but Albion refused to go down without a fight and their persistence was rewarded 13 minutes from time when Ellington headed home a Greening corner.
But it was of little comfort in the end for Albion who have plunged deeper into trouble after their latest defeat.