Invicta trailed 3-1 early on but recovered superbly to lead 8-5 at the start of what proved to be an action-packed third period. That prompted a Cheltenham revival as they pulled up to 9-9 with a breakaway goal by Will Rayson, who scored again shortly afterwards.
There were no more goals. A highly-charged final quarter produced just one exclusion and three time-outs.
Later, Welsh Wanderers pulled off a remarkable 14-13 victory over Polytechnic, scoring six times without reply in the fourth period.
Meanwhile, at Matlock, champions Manchester scored five without reply in the final period to see off Sheffield 12-4. Lancaster's 18-12 defeat of Solihull featured an outstanding nine-goal contribution from John Pratt.
In men's Division 4, Newport improved their hopes of a top five place when a goal in the last second by Matt Veale salvaged an 11-11 draw with the British Army. Southampton maintained their 100 per cent record from six games, beating Rotherham 12-5. Charles Roberts' four goals took his tally for the season to 31.
At Matlock, Tyldesley's Addison Brown scored nine as Tyldesley outplayed York City 17-4 for their first win of the season. Bridgefield also notched their first victory - 12-7 against Sheffield Dolphins.
Photo (Trevor Hyde): An almost cap-less John Pratt on the way to scoring nine for Lancaster against Solihull.