Disclosed are applicators and methods injecting of a liquid anesthetic into a dental patient with no or minimal pain. In accordance with one embodiment the applicator is for intraligamentary injection and includes an elongated, thin member having an open distal free formed of a resilient and somewhat conformable material suitable for producing a substantially fluid-tight interface with the anatomic structures at the gingival sulcus to inject the anesthetic therein. In another embodiment the applicator includes a flexible skirt surrounding a sharpened cannula, with the cannula being movable with respect to the skirt. The skirt is arranged to receive the anesthetic to anesthetize the gum, whereupon the cannula can then pierce the gum to inject the anesthetic into the underlying anatomic structure.