Westcarr fired home the only goal of the game from just inside the penalty area after 11 minutes following good work from former United academy graduate James Baxendale.
Both sides enjoyed a host of chances to add to the scoreline but were denied by wayward finishing or great goalkeeping, Leeds stopper Paddy Kenny producing the save of the game to keep out Saddlers substitute Romaine Sawyers in the second half.
Shrewsbury and Bolton played out a 3-3 draw in an action-packed pre-season friendly at the Greenhous Meadow.
Marvin Sordell's powerful strike and Chris Eagles' well-taken finish sandwiched John Marsden's equaliser, before Sordell added his second with another sunning effort just before half-time to hand the Trotters a 3-1 advantage.
Yet League One Town hit back after the break to claim a draw, Paul Parry matching Sordell's eye for the spectacular before loan signing Akwasi Asante nicked the ball off Zat Knight to duly draw the Shropshire outfit level 13 minutes from time.
Barnsley twice came behind to share a 2-2 pre-season draw with Wolves at Oakwell.
Zeli Ismail converted Jake Cassidy's cross after just three minutes to put Wanderers - League One title favourites following back-to-back relegations - ahead after just three minutes.
But the Tykes were quickly level as Jacob Mellis converted neatly from 12 yards.
Danny Batth's flicked header put Wolves back in front in the 20th minute but hosts Barnsley levelled for a second time just before the hour mark, Chris O'Grady turning and slotting home after a well-worked move.
Bournemouth warmed up for the visit of Real Madrid with a 2-1 defeat to Woking.
Despite a sold-out clash with the Spanish giants due to start just 26 hours after the final whistle blew at the Kingfield Stadium, Eddie Howe named a strong starting line-up which included summer signing Ian Harte.
They took just six minutes to open the scoring, Jayden Stockley netting against his former club at the far post. That lead lasted just three minutes, though, as Gavin McCallum was left with the easiest of finishes to level things up.
And the home side had the final say with five minutes remaining when Lyle Taylor's low drive from outside the box found a way past Shwan Jalal to leave Howe focusing on Sunday's high-profile clash.
Former Manchester United trainee Brandy turned his man inside the box and finished after being put through by Daryl Westlake in the third minute.
The League One side were good value for their win and Jamie Murphy, Chris Porter and Kevin McDonald all wasted superb chances to extend the lead.
Mansfield improved in the second half and half-time substitutes Lee Stevenson and Amari Morgan-Smith both tested George Long in the Blades goal but an equaliser never really looked forthcoming.
Two goals from Danny Ings helped Burnley to a comfortable 4-1 friendly win at Carlisle.
Having previously netted twice in a win over Cork the former Bournemouth forward scored another double after Ross Wallace's opener as the visitors raced into a three-goal lead inside 22 minutes.
Lee Miller's penalty was then superbly kept out by summer signing Tom Heaton before Junior Stanislas added a fine fourth with a clever chip.
And straight from the restart Lewis Guy drilled home a consolation for the League One outfit.
A top-class strike from Bristol City's Liam Kelly was enough to beat Forest Green 1-0 at The New Lawn.
The Robins fans who made the short trip were celebrating after just 10 minutes when Kelly's curling 20-yard effort flew in via the far post.
And Kelly could have grabbed a second but fired over the bar after a smart lay-off from Sam Baldock before the break.
Trialist Marlon Harewood's powerful drive was only kept out by a fine block by Dale Bennett and, at the other end, City were let off when Ben Wright and then Yan Klukowski both rattled the woodwork.