Shearer rose above Gianluca Festa in the penalty box to carefully place a header into the left-hand corner of the Middlesbrough net, giving Schwarzer little chance.
One of the bikes will return to the Harley-Davidson museum in Milwaukee, while the other will be auctioned off at the festa with proceeds supporting the Good Samaritan Foundation.
Even the dismissal of Boro's Gianluca Festa for a second bookable offence in the space of two minutes came too close to the end of the match to inspire a breakthrough.