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Sharding is a promising blockchain scaling solution. But it currently suffers from high latency and low throughput when it comes to cross-shard transactions, i.e., transactions that require coordination from multiple shards. The root cause of these limitations arise from the use of the classic two-phase commit protocol, which involves locking assets for extended periods of time. This paper presents Rivet, a new paradigm for blockchain sharding that achieves lower latency and higher throughput for cross-shard transactions. Rivet has a single reference shard running consensus, and multiple worker shards maintaining disjoint states and processing a subset of transactions in the system. Rivet obviates the need for consensus within each worker shard, and as a result, tolerates more failures within a shard and lowers communication overhead. We prove the correctness and security of Rivet. We also propose a more realistic framework for evaluating sharded blockchains by creating a benchmark based on real Ethereum transactions. An evaluation of our prototype implementation of Rivet and the baseline two-phase commit, atop 50+ AWS EC2 instances, using our evaluation framework demonstrates the latency and throughput improvements for cross-shard transactions.