In this paper, we present a sentence simplification method and demonstrate its use to improve intent determination and slot filling tasks in spoken language understanding (SLU) systems. This research is motivated by the observation that, while current statistical SLU models usually perform accurately for simple, well-formed sentences, error rates increase for more complex, longer, more natural or spontaneous utterances. Furthermore, users familiar with web search usually formulate their information requests as a keyword search query, suggesting that frameworks which can handle both forms of inputs is required. We propose a dependency parsing-based sentence simplification approach that extracts a set of keywords from natural language sentences and uses those in addition to entire utterances for completing SLU tasks. We evaluated this approach using the well-studied ATIS corpus with manual and automatic transcriptions and observed significant error reductions for both intent determination (30% relative) and slot filling (15% relative) tasks over the state-of-the-art performances.