Browne, given an opportunity from the start for the first time in seven matches, kept his eye on the ball to smash the Glovers into a first-half lead.
Southampton loanee Olomola wrapped up three points in the second period with his sixth goal in Yeovil colours.
Manager Darren Way made two other changes to the side that suffered a 2-0 defeat at Newport County last weekend.
Omar Sowunmi and Bevis Mugabi slotted into defence, replacing Sid Nelson – who underwent an operation on a broken nose on Thursday – and Tom James.
An entertaining beginning saw both sides go close in the opening 14 minutes.
Crewe’s George Cooper was denied an effort on goal by a superb challenge from Mugabi and Sowunmi threw himself in front of the follow up to set up a Yeovil attack.
It resulted in Francois Zoko’s deflected shot from close range falling kindly for away stopper Dave Richards, who in turn set up another attack for the visitors.
Cooper was again instrumental in the Alex progressing downfield and his slide-rule pass was collected by experienced frontman Chris Porter but his toe poke shaved the outside of the post.
Keeping up with the Chuckle Brothers ‘to me, to you’ theme on the chance front, a free-flowing Town move saw Browne cheekily back heel to Olomola whose right-footed strike flashed past the far post.
Then the first goal of the game came.
Otis Khan’s cross from the left flicked up off the boot of Zoko and sat up nicely for Browne to finish with a sweet volley.
It noticeably gave the Barbuda and Antigua international a lease of confidence, as he fired over shortly after before winning the ball back from ex-Glovers loanee Zoumana Bakayogo and teeing up Zoko who shot low into the gloves of Richards.
Crewe worked hard to find an equaliser prior to the interval and they may have levelled if not for a number of good stops from Artur Krysiak.
The Polish stopper did brilliantly to tip away Eddie Nolan’s attempt from outside the box and foiled Callum Ainley seconds later.
Krysiak made a third save in quick succession, pushing away Jordan Bowery’s glancing header before Cooper dragged a shot wide at the end of a busy half.
Things settled down after the break with neither keeper troubled until Olomola netted a vital second for the Glovers.
The 20-year-old controlled Ryan Dickson’s deep delivery and his shot into the ground clipped an outstretched Crewe leg and looped into the net.
Crewe almost reduced the deficit when Nolan’s powerful header crashed against the crossbar but after that it was a relatively straightforward final half-hour for Town.
Khan had a chance to convert from six yards however slipped at the last, Browne saw his 25-yarder beaten away and Zoko found the back of the Thatchers terrace from a good position.
With five minutes to go, Browne hit low at Richards when he probably should have squared it and substitute Sam Surridge tried to get in on the goals, but was thwarted three times by some good defending and goalkeeping.
All in all, it was a solid display from back to front as the Green and Whites bounced back from consecutive defeats and rose to 17th in the table.
Yeovil Town: Krysiak, Mugabi, Sowunmi, N.Smith, Dickson, Browne, Bailey, C.Smith, Khan (Santos 89), Olomola (Surridge 74), Zoko.
Bookings: Zoko 89.
Subs not used: Maddison, Davies, James, Worthington, Gray.
Crewe Alexandra: Richards, Ng, Raynes, Nolan, Bakayogo (Pickering 79), Cooper, Ainley (Dagnall 61), Grant, Lowery, Bowery (Kirk 79), Porter.
Subs not used: Garratt, Walker, Reilly, Stubbs.