Simon Walton also impressed while Aussie Joel Griffiths turned in a good game to give Kevin Blackwell food for thought ahead of Sunday's game at Preston.
Boro fielded a team with no less than seven players with first eleven experience. Returning from injury were Lee Cattermole and Tony McMahon, while Malcolm Christie played 75 minutes.
In fact, it was the former Derby County and England U21 striker who gave Boro the lead 10 minutes into the second half.
But the lead lasted less than 10 minutes as Leeds hit back through Jonathan Howson.
Leeds had started the brighter and were always a threat down the right-hand side. Griffiths had given Walton an early opportunity but the youngster shot over.
Griffiths should then have done better when gifted with a chance with an error by Wheater but he wasted it from only 6-yards out.
Baily Cranfield delivered a free-kick into the area and the unfortunate Wheater nearly scored an own goal but David Knight pulled off a great save.
Boro took the lead when Christie made a cross-come-shot, deceiving Mark Wilberforce in the Leeds goal. Then United hit back when Howson took adavantage of a McMahon slip in the area and buried his chance from close angle.
Griffiths found Danny Pugh and Jermaine Beckford in the area and what should have been a simple goal turned into a calamity as they collided and the chance went begging.
Pugh was booked for a challenge on McMahon soon after. Wilberforce made fine saves from Craddock and Owens and Hutchinson fired just over from close in.
Both sides had opportunities to win but it finished even. The Whites second string now meet Aston Villa on Thursday.
United: Wilberforce, Madden, Harding, Cranfield, Walton, Howson, Stone, Einarsson, Beckford, Griffiths, Pugh.
Subs: Bailey, Gardner, Serrant, Ameobi, Hutton.
Boro: Knight, McMahon, Grounds, Cattermole (Owens 71), Davies, Wheater, Liddle, Kennedy, Christie (Hutchinson 75), Craddock, Johnson.
Unused Subs: Williams, Mulligan, Walker.