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Basso the hero as City stay top
Basso: Congratulated by Orr after penalty save
The visitors were handed a spot-kick against the run of play five minutes before half-time when Tommy Smith's heels were clipped by Michael McIndoe - but Henderson's penalty was superbly saved by Basso's outstretched hand.
On the balance of play a draw was a fair result after the Robins had dominated the first half, while the visitors were the more effective outfit in the second.
The point was enough to keep the home side top of the league despite Stoke's victory on Tuesday, while Watford, who have now drawn their last five games, remain third.
The two teams may both be among the contenders for promotion but their contrasting styles were apparent within moments of the whistle.
City, last defeated at home in the league on November 24, preferred a patient passing game while as expected, the visitors adopted a more direct approach, utilising Leigh Bromby's huge long throws.
With so much at stake it was no surprise to see both teams begin cautiously and it took 15 minutes for Jobi McAnuff to spurn the game's first chance.
From then on the home side were by far the better side and twice Lee was extended by long-range efforts from Marvin Elliott.
The first was a low drive destined for the bottom-left corner which Lee tipped around the post and the second a more powerfully struck effort made all the more difficult by the swirling winds in the south-west.
But the resolute Hornets boast the league's best away record for a reason and it was they who had the best chance of the game when referee Andre Marriner pointed to the spot, only for Basso to guess correctly.
The Watford striker's day could have got even worse moments later after a dangerous lunge on Lee Johnson and he was lucky to escape with a yellow card.
Johnson, the manager's son, quickly exacted revenge on Danny Shittu to earn himself a caution and failed to return after the break after being replaced by Nick Carle.
The second period began much like the first and again it was Adrian Boothroyd's side who had the first real opportunity, John Eustace delivering a pinpoint centre but Bromby's header flew the wrong side of the right post.
There was style but no substance to City's play as Watford's muscular defence coped more comfortably with their offensive threat than in the first half.
When they finally did breach the Hornets' rearguard, their finishing let them down as Dele Adebola got in between his marker and Lee only to head Jamie McAllister's cross woefully wide.
It was Watford who finished the stronger and John-Joe O'Toole and McAnuff both had chances to win it late on as they were forced to settle for a point each - a result which will be welcomed most by rivals Stoke and West Brom.