Tigers led twice, but went behind deep into the second half before Derrell Olpherts’ try, converted from the touchline by Richardson, levelled the scores, writes Peter Smith.
Both teams missed with drop goal efforts in extra-time, but Richardson, with his fourth attempt of the game, won it in the 88th minute.
Richardson, who is out of contract at the end of this season, is two games into his comeback from a neck fracture suffered in Betfred Super League round one and Radford is hopeful his future will be resolved in the next two to three weeks.
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“It’s brilliant for him,” he said of the former St Helens scrum-half’s match-winning contribution.
“He has not only had the neck thing, he came back to play reserves and picked up another injury. To see him back on the field, doing what he does, is pleasing.
“He’s good around the place, I like him.”
Tigers lost full-back Ryan Hampshire to a knee injury early in the second half and Adam Milner - who took a bang to the head - and Liam Watts also had lengthy spells off the field.
Radford said: “I’m pleased to come out of the other end of it.
“Some of the stuff that got thrown at us, losing Rocky and Adz [Milner] could have had some really detrimental effects, but I thought we stuck at it fantastically.
“The last game, against Toulouse, was a really big win for us and to back it up was special.
“We got our reward for aiming up and sticking at it.
“We had two interchanges we couldn’t use and we had people playing out of position, but their effort and commitment was fantastic.”
Sunday’s 17-16 win kept Tigers in the hunt for fifth place and avenged a 44-12 defeat in Perpignan earlier in the season.
Radford added: “That’s the beauty of this game, you get to right some wrongs.
“They can sleep easy knowing they’ve done that.”