The visitors made a bright start, before Breuer's intervention gave the Magpies the lead on the night. The defender attempted to clear Laurent Robert's tenth minute cross, but managed only to divert the ball past Brian Vandenbussche and into the net.
Shola Ameobi went close to doubling the lead before skipper Shearer did so with 25 minutes on the clock.
Kieron Dyer was fouled 25 yards from goal and from the resulting free-kick Robert rolled the ball to Shearer and he rifled a low shot into the corner of the net, despite the best efforts of Vandenbussche.
Shortly afterwards Ameobi's header from another Robert delivery grazed the outside of the post.
Heerenveen rarely threatened up to half-time, with Arnold Bruggink firing a rare chance just wide of the far post.
The Magpies brought on Jermaine Jenas for Dyer at the interval, with the opening minutes of the second half seeing little action in either goalmouth.
Another sub, James Milner, almost made it 3-0 midway through the second period, but with ten minutes to play Heerenveen were handed a lifeline.