Given a text and a pattern over an alphabet, the classic exact matching problem searches for all occurrences of the pattern in the text. Unlike exact matching, order-preserving pattern matching (OPPM) considers the relative order of elements, rather than their exact values. In this paper, we propose efficient algorithms for the OPPM problem using the “duel-and-sweep” paradigm. For a pattern of length $m$ and a text of length $n$, our serial algorithm runs in $O(n + m \log{m})$ time, and our parallel algorithm runs in $O(\log^2{m})$ time and $O(n \log^2{m})$ work with $O(\log{m})$ time and $O(m \log{m})$ work pattern preprocessing on the Priority Concurrent Read Concurrent Write Parallel Random-Access Machines (P-CRCW PRAM).