The bad weather forced a pitch inspection before this league fixture could go ahead.
But although the surface was going to be heavy the Badgers were keen to get back into action after a three-week break.
United won the toss and started with the wind behind them and they got their first effort on goal through Tomlinson after 10 minutes, his shot just clearing the angle.
Two minutes later, with Worsbrough finding difficulty getting out of their half against the wind, Liam Cartledge turned a defender and got off a shot that bobbled wide of the left-hand upright.
Worsbrough responded but Jonny Jackson's drive following a free-kick was blocked by Ian Bagshaw.
Local supporters called for a penalty on 19 minutes when Bagshaw tangled with Gary Strudwick, but the referee was having nothing of it.
A good move soon after saw the hosts work the ball out and Jody Barford was called upon to make his first save of the game.
At the other end, Kevin Noteman pulled the ball back for Simon Hennessy to hit a low, hard shot just wide of goal.
But a minute later Retford were in front as a mistake in the Worsbrough defence was punished by Liam Cartledge, who set up Tomlinson to plant the ball past Chris Driver for the opener.
With the wind against the Bagders after the break, they stepped up the tempo in search of a second before the turnaround.
Danny Scott put in a superb cross after a good run down the left and Simon Hennessy got off a powerful header but it flew inches wide.
More frustration came when another cross from Scott dropped between Kevin Noteman and Hennessy at the far post when a touch from either would have brought a goal.
A cracking shot from Rob Burton from a free-kick was met with an equally good save from Driver.
Another free-kick taken by brother Chris Burton found Ian Bagshaw but his header was also saved.
The second half started in a hailstorm, and, as predicted, the hosts were pushing with the wind now behind them.
The first effort, though, came from Retford – Hennessy centred and Tomlinson was not far off target.
But the ball was quickly back in the Retford half and Bagshaw got in a timely block to deny Alex Gillespie.
However, Bridge were soon level as a free-kick was floated to the back post where Strudwick came in behind the defence and sent a header past Barford.
Just four minutes later the lead was restored, when wide man Scott was sent on his way up the left by Kevin Noteman.
His cross was met at the back post by Hennessy whose shot hit the keeper and deflected up onto the cross bar, down onto the post and across to Tomlinson.
That left the forward with the simplest of tasks of blasting the ball into the back of an unguarded net.
But Worsbrough were not done as Ryan Poskit got past Bagshaw and only a brilliantly timed tackle in the box by Lee Smith cut out what looked to be a certain goal.
The heavy pitch was taking its toll and legs were tiring as United's defence worked hard and at times battled desperately to keep out their opponents.
Visiting hearts stopped in time added on as Gillespie managed to get behind the Badgers defence and as Barford came out to narrow the angle, he lost his footing, but the home player shot into the side netting.
Retford are next in action tomorrow when they will hope for another victory as South Normanton Athleitc make the trip to Cannon Park (3pm).