In educational assessment, rubrics are a key tool because they define clear criteria for evaluating learner responses and specify the evidence required. Yet, in research on automatic short-answer scoring, rubrics are seldom employed as explicit scoring references and, when they are, they are typically treated only as supplementary inputs. This study contrasts this by exploring the usage of rubrics as explicit scoring anchors in automatic short-answer scoring. It introduces a task definition for rubric-based automatic short-answer scoring, a version of short-answer scoring that uses scoring rubrics as scoring references. As an approach for implementing rubric-based short answer scoring, we introduce the idea of guided rubric answer alignment and provide two concrete architectures based on this, GRAASP and ToLeGRAA. Both are novel transformer-based architectures that use attention mechanisms to predict the alignment between student answers and rubric criteria. We compare them to multiple baselines using ALICE-LP, a novel German short-answer scoring dataset collected from formative assessments in authentic German school contexts, and the widely used ASAP-SAS dataset, collected at American schools. For both datasets, GRAASP and ToLeGRAA achieve highly competitive performance. By explicitly aligning learner responses with rubric criteria when assigning scores, these models demonstrate the feasibility of rubric-based short-answer scoring. This finding underscores the high potential of integrating rubric-driven scoring models into educational assessment.