The Blues sealed the three points after edging a second half that produced five goals.
George Hirst (50 minutes – penalty) and Michael Jacobs (68) handed the home side a 2-0 lead, before Teddy Bishop (70) and substitute Ben House (78) got the Imps back on level terms.
However, Pompey substitute Ronan Curtis restored the Blues’ advantage on 82 minutes when he made the most of goalkeeper Jordan Wright’s inability to hang on to Sean Raggett’s drilled effort to bag his eighth goal of the season.
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